Journal of the London Mathematical Society-Second Series最新文献
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Fully noncentral Lie ideals and invariant additive subgroups in rings
环上的完全非中心李理想和不变加性子群
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-18
DOI: 10.1112/jlms.70127
Eusebio Gardella, Tsiu-Kwen Lee, Hannes Thiel
{"title":"Fully noncentral Lie ideals and invariant additive subgroups in rings","authors":"Eusebio Gardella, Tsiu-Kwen Lee, Hannes Thiel","doi":"10.1112/jlms.70127","DOIUrl":"https://doi.org/10.1112/jlms.70127","url":null,"abstract":"<p>We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≠</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$ne 2$</annotation>\u0000 </semantics></math> where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solvability and uniqueness of solution of generalized ★ $star$ -Sylvester equations with arbitrary coefficients
任意系数广义★$star$ -Sylvester方程解的可解性和唯一性
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-18
DOI: 10.1112/jlms.70129
Fernando De Terán, Bruno Iannazzo
{"title":"Solvability and uniqueness of solution of generalized \u0000 \u0000 ★\u0000 $star$\u0000 -Sylvester equations with arbitrary coefficients","authors":"Fernando De Terán, Bruno Iannazzo","doi":"10.1112/jlms.70129","DOIUrl":"https://doi.org/10.1112/jlms.70129","url":null,"abstract":"<p>We analyze the consistency and uniqueness of solution of the generalized <span></span><math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math>-Sylvester equation <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>X</mi>\u0000 <mi>B</mi>\u0000 <mo>+</mo>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>X</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 <mi>D</mi>\u0000 <mo>=</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$AXB+CX^star D=E$</annotation>\u0000 </semantics></math>, with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>,</mo>\u0000 <mi>B</mi>\u0000 <mo>,</mo>\u0000 <mi>C</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$A,B,C, D$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> being complex matrices (and <span></span><math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math> being either the transpose or the conjugate transpose). In particular, we obtain characterizations for the equation to have at most one solution and to be consistent for any right-hand side. Such characterizations are given in terms of spectral properties of the matrix pencils <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mtable>\u0000 <mtr>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mtd>\u0000 <mtd>\u0000 <msup>\u0000 <mi>B</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mtd>\u0000 </mtr>\u0000 <mtr>\u0000 <mtd>\u0000 <mi>A</mi>\u0000 </mtd>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mtd>\u0000 </mtr>\u0000 </mtable>\u0000 </mfenced>\u0000 <annotation>$left[begin{smallmatrix}lambda D^star & B^star A & lambda Cend{smallmatrix}right]$</annota","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shift orbits for elementary representations of Kronecker quivers
克罗内克颤的初等表示的移位轨道
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-11
DOI: 10.1112/jlms.70122
Daniel Bissinger
{"title":"Shift orbits for elementary representations of Kronecker quivers","authors":"Daniel Bissinger","doi":"10.1112/jlms.70122","DOIUrl":"https://doi.org/10.1112/jlms.70122","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$r in mathbb {N}_{geqslant 3}$</annotation>\u0000 </semantics></math>. We denote by <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <annotation>$K_r$</annotation>\u0000 </semantics></math> the wild <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-Kronecker quiver with <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> arrows <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <mn>1</mn>\u0000 <mo>⟶</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$gamma _i colon 1 longrightarrow 2$</annotation>\u0000 </semantics></math> and consider the action of the group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mo>⊆</mo>\u0000 <mo>Aut</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$G_r subseteq operatorname{Aut}(mathbb {Z}^2)$</annotation>\u0000 </semantics></math> generated by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>⟶</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variational stabilization of degenerate p $p$ -elasticae
简并p$ p$ -弹性模型的变分稳定性
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-11
DOI: 10.1112/jlms.70096
Tatsuya Miura, Kensuke Yoshizawa
{"title":"Variational stabilization of degenerate \u0000 \u0000 p\u0000 $p$\u0000 -elasticae","authors":"Tatsuya Miura, Kensuke Yoshizawa","doi":"10.1112/jlms.70096","DOIUrl":"https://doi.org/10.1112/jlms.70096","url":null,"abstract":"<p>A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-elasticae. It was known that in the nondegenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$pin (1,2]$</annotation>\u0000 </semantics></math>, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$pin (2,infty)$</annotation>\u0000 </semantics></math> there emerge uncountably many local minimizers with diverging energy.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Size-Ramsey numbers of graphs with maximum degree three
最大度为3的图的大小拉姆齐数
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-11
DOI: 10.1112/jlms.70116
Nemanja Draganić, Kalina Petrova
{"title":"Size-Ramsey numbers of graphs with maximum degree three","authors":"Nemanja Draganić, Kalina Petrova","doi":"10.1112/jlms.70116","DOIUrl":"https://doi.org/10.1112/jlms.70116","url":null,"abstract":"<p>The size-Ramsey number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mi>r</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$hat{r}(H)$</annotation>\u0000 </semantics></math> of a graph <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> is the smallest number of edges a (host) graph <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> can have, such that for any red/blue colouring of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, there is a monochromatic copy of <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. Recently, Conlon, Nenadov and Trujić showed that if <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> is a graph on <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> vertices and maximum degree three, then <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mi>r</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mi>O</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>8</mn>\u0000 <mo>/</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$hat{r}(H) = O(n^{8/5})$</annotation>\u0000 </semantics></math>, improving upon the upper bound of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70116","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ergodic averages along sequences of slow growth
沿缓慢增长序列的遍历平均值
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-11
DOI: 10.1112/jlms.70124
Kaitlyn Loyd, Sovanlal Mondal
{"title":"Ergodic averages along sequences of slow growth","authors":"Kaitlyn Loyd, Sovanlal Mondal","doi":"10.1112/jlms.70124","DOIUrl":"https://doi.org/10.1112/jlms.70124","url":null,"abstract":"<p>We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math> denotes the number of prime factors of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$ n$</annotation>\u0000 </semantics></math> counted with multiplicities. It was previously shown that a pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> functions does not hold along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. We classify the strength of this divergence by proving a double-logarithmic pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> functions along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. This contrasts the behavior of Khintchine-type averages, for which, under any weaker form of averaging, there exists a bounded measurable function for which almost everywhere convergence fails. Moreover, we show that certain perturbations of increasing subpolynomial sequences fail to satisfy a pointwise ergodic theorem, yielding natural new examples of such sequences.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70124","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Einstein metrics on aligned homogeneous spaces with two factors
有两个因子的对齐齐次空间上的爱因斯坦度量
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-10
DOI: 10.1112/jlms.70120
Jorge Lauret, Cynthia Will
{"title":"Einstein metrics on aligned homogeneous spaces with two factors","authors":"Jorge Lauret, Cynthia Will","doi":"10.1112/jlms.70120","DOIUrl":"https://doi.org/10.1112/jlms.70120","url":null,"abstract":"<p>Given two homogeneous spaces of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$G_1/K$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$G_2/K$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$G_1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$G_2$</annotation>\u0000 </semantics></math> are compact simple Lie groups, we study the existence problem for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$G_1times G_2$</annotation>\u0000 </semantics></math>-invariant Einstein metrics on the homogeneous space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$M=G_1times G_2/K$</annotation>\u0000 </semantics></math>. For the large subclass <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathcal {C}$</annotation>\u0000 </semantics></math> of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and nonexistence pieces of <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathcal {C}$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rigidity of quantum algebras
量子代数的刚性
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-08
DOI: 10.1112/jlms.70118
Akaki Tikaradze
{"title":"Rigidity of quantum algebras","authors":"Akaki Tikaradze","doi":"10.1112/jlms.70118","DOIUrl":"https://doi.org/10.1112/jlms.70118","url":null,"abstract":"<p>Given an associative <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>-algebra <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, we call <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> strongly rigid if for any pair of finite subgroups of its automorphism groups <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>$G, H$</annotation>\u0000 </semantics></math>, such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>G</mi>\u0000 </msup>\u0000 <mo>≅</mo>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>H</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$A^Gcong A^H$</annotation>\u0000 </semantics></math>, then <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid. We also solve the inverse Galois problem for a wide class of rational Cherednik algebras that includes all (simple) classical generalized Weyl algebras, and also for quantum tori. Finally, we show that the Picard group of an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional quantum torus is isomorphic to the group of its outer automorphisms.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher order Lipschitz Sandwich theorems
高阶李普希茨三明治定理
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-07
DOI: 10.1112/jlms.70121
Terry Lyons, Andrew D. McLeod
{"title":"Higher order Lipschitz Sandwich theorems","authors":"Terry Lyons, Andrew D. McLeod","doi":"10.1112/jlms.70121","DOIUrl":"https://doi.org/10.1112/jlms.70121","url":null,"abstract":"<p>We investigate the consequence of two <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Lip</mi>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${mathrm{Lip}}(gamma)$</annotation>\u0000 </semantics></math> functions, in the sense of Stein, being close throughout a subset of their domain. A particular consequence of our results is the following. Given <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>></mo>\u0000 <mi>ε</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$K_0 > varepsilon > 0$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>></mo>\u0000 <mi>η</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$gamma > eta > 0$</annotation>\u0000 </semantics></math>, there is a constant <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>=</mo>\u0000 <mi>δ</mi>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>,</mo>\u0000 <mi>η</mi>\u0000 <mo>,</mo>\u0000 <mi>ε</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$delta = delta (gamma,eta,varepsilon,K_0) > 0$</annotation>\u0000 </semantics></math> for which the following is true. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Sigma subset {mathbb {R}}^d$</annotation>\u0000 </semantics></math> be closed and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>h</mi>\u0000 <mo>:</mo>\u0000 <mi>Σ</mi>\u0000 <mo>→</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$f, h: Sigma rightarrow {mathbb {R}}$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143571227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2
2次Siegel尖形式的傅里叶系数界和全局上模
IF 1
2区 数学
Journal of the London Mathematical Society-Second Series
Pub Date : 2025-03-07
DOI: 10.1112/jlms.70119
Félicien Comtat, Jolanta Marzec-Ballesteros, Abhishek Saha
{"title":"Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2","authors":"Félicien Comtat, Jolanta Marzec-Ballesteros, Abhishek Saha","doi":"10.1112/jlms.70119","DOIUrl":"https://doi.org/10.1112/jlms.70119","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math> be an <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-normalized Siegel cusp form for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Sp</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>${rm Sp}_4({mathbb {Z}})$</annotation>\u0000 </semantics></math> of weight <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> that is a Hecke eigenform and not a Saito–Kurokawa lift. Assuming the generalized Riemann hypothesis, we prove that its Fourier coefficients satisfy the bound <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>a</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>F</mi>\u0000 <mo>,</mo>\u0000 <mi>S</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mo>≪</mo>\u0000 <mi>ε</mi>\u0000 </msub>\u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mi>k</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>4</mn>\u0000 <mo>+</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 </msup>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>4</mn>\u0000 <mi>π</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>k</mi>\u0000 </msup>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mfrac>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70119","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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