Journal of Algebra最新文献

{"title":"A new generalization of the McKay conjecture for p-solvable groups","authors":"Huimin Chang,&nbsp;Ping Jin","doi":"10.1016/j.jalgebra.2026.01.030","DOIUrl":"10.1016/j.jalgebra.2026.01.030","url":null,"abstract":"<div><div>Let <em>P</em> be a Sylow <em>p</em>-subgroup of a finite <em>p</em>-solvable group <em>G</em>, where <em>p</em> is a prime. Using a normal <em>p</em>-series <span><math><mi>N</mi></math></span> of <em>G</em>, we introduce the notion of <span><math><mo>(</mo><mi>N</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-stable characters and prove that <em>G</em> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>P</mi><mo>)</mo></math></span> have equal numbers of such characters, which gives a new generalization of the McKay conjecture for <em>p</em>-solvable groups. Also, we establish a canonical bijection between these characters in the case where <em>G</em> has odd order. Our proofs depend heavily on the theory of self-stabilizing pairs founded by M.L. Lewis, as well as some new results on <em>π</em>-special characters due to I.M. Isaacs and G. Navarro.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 381-396"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171944","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}

{"title":"Bitangents to symmetric quartics","authors":"Candace Bethea,&nbsp;Thomas Brazelton","doi":"10.1016/j.jalgebra.2025.12.010","DOIUrl":"10.1016/j.jalgebra.2025.12.010","url":null,"abstract":"<div><div>Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is <em>symmetric</em> if it admits non-trivial automorphisms. The classification of (necessarily finite) groups appearing as automorphism groups of non-singular curves of genus three dates back to the last decade of the 19th century. As these groups act on the quartic via projective linear transformations, they induce symmetries on the 28 bitangents. Given such an automorphism group <span><math><mi>G</mi><mo>=</mo><mtext>Aut</mtext><mo>(</mo><mi>C</mi><mo>)</mo></math></span>, we leverage tools from equivariant homotopy theory to prove that the <em>G</em>-orbits of the bitangents are independent of the choice of <em>C</em>, and we compute them for all twelve types of smooth symmetric planar quartic curves. We further observe that techniques deriving from equivariant homotopy theory directly reveal patterns which are not obvious from a classical moduli perspective.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 397-426"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171943","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}

{"title":"Harish-Chandra modules over the higher rank W-algebra W(2,2)","authors":"Haibo Chen","doi":"10.1016/j.jalgebra.2026.01.036","DOIUrl":"10.1016/j.jalgebra.2026.01.036","url":null,"abstract":"<div><div>In this paper, using the theory of <span><math><mi>A</mi></math></span>-cover developed in <span><span>[2]</span></span>, <span><span>[3]</span></span>, we completely classify all simple Harish-Chandra modules over the higher rank <em>W</em>-algebra <span><math><mi>W</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. According to this result, we give a classification of all simple Harish-Chandra modules over some related higher rank Lie (super)algebras, such as higher rank deformed <span><math><msub><mrow><mi>bms</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> algebras, the subalgebra of higher rank super-Galilean conformal algebras and so on. Moreover, we obtain the classification of simple Harish-Chandra modules over the classical <em>W</em>-algebra <span><math><mi>W</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> studied in <span><span>[8]</span></span>, <span><span>[14]</span></span>, <span><span>[19]</span></span> as a byproduct.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 427-447"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171942","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}

{"title":"Geodesic languages for rational subsets and conjugates in virtually free groups","authors":"André Carvalho ,&nbsp;Pedro V. Silva","doi":"10.1016/j.jalgebra.2025.12.034","DOIUrl":"10.1016/j.jalgebra.2025.12.034","url":null,"abstract":"<div><div>We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements in a rational subset of a virtually free group is context-free. As a corollary, the doubly generalized conjugacy problem is decidable for rational subsets of finitely generated virtually free groups: there is an algorithm taking as input two rational subsets <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of a virtually free group that decides whether there is one element of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> conjugate to an element of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. For free groups, we prove that the same problem is decidable with rational constraints on the set of conjugators.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 263-286"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171956","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}

{"title":"K1-Stability of symplectic modules over monoid algebras","authors":"Rabeya Basu,&nbsp;Maria Ann Mathew","doi":"10.1016/j.jalgebra.2025.12.033","DOIUrl":"10.1016/j.jalgebra.2025.12.033","url":null,"abstract":"<div><div>Let <em>R</em> be a regular ring of dimension <em>d</em> and <em>L</em> be a <em>c</em>-divisible monoid. If <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mi>Sp</mi></mrow><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is trivial and <span><math><mi>k</mi><mo>≥</mo><mi>d</mi><mo>+</mo><mn>2</mn></math></span>, then we prove that the symplectic group <span><math><msub><mrow><mi>Sp</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>[</mo><mi>L</mi><mo>]</mo><mo>)</mo></math></span> is generated by elementary symplectic matrices over <span><math><mi>R</mi><mo>[</mo><mi>L</mi><mo>]</mo></math></span>. When <span><math><mi>d</mi><mo>≤</mo><mn>1</mn></math></span> or <em>R</em> is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of <span><span>[14]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 185-208"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172049","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}

{"title":"The normal bundle of a rational curve is determined by specific properties of the curve's singularities","authors":"Maria-Grazia Ascenzi","doi":"10.1016/j.jalgebra.2026.01.029","DOIUrl":"10.1016/j.jalgebra.2026.01.029","url":null,"abstract":"<div><div>Let <em>D</em> denote a rational curve of degree <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>≥</mo><mn>4</mn></math></span>, with only ordinary singularities and spanning <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. We consider the normal bundle <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> where <em>φ</em> denotes a generically one-to-one parametrization of <em>D</em>. We study the parameter <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn><mi>D</mi></mrow></msub></math></span> that controls the splitting of <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> in terms of line bundles. We find that specific properties of <em>D</em>, related to its singular points, characterize <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn><mi>D</mi></mrow></msub></math></span>. These properties are: the multiplicities and the auxiliary curve associated to the largest multiplicity.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 209-220"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172050","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}

{"title":"Ideals invariant under powers of derivations","authors":"Cătălin Ciupercă","doi":"10.1016/j.jalgebra.2026.01.025","DOIUrl":"10.1016/j.jalgebra.2026.01.025","url":null,"abstract":"<div><div>If <em>δ</em> is a derivation on a commutative noetherian ring <em>A</em> containing a field of characteristic zero and <em>k</em> is a positive integer, we study the ideals <em>I</em> of <em>A</em> satisfying <span><math><mi>δ</mi><msup><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><mo>⊆</mo><mi>I</mi></math></span>. Most results are concerned with the behavior of their integral closures, rational powers, and arbitrary saturations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 29-43"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098442","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}

{"title":"Rational and elliptic surface singularity of fiber type","authors":"R.V. Gurjar ,&nbsp;M. Miyanishi","doi":"10.1016/j.jalgebra.2026.01.038","DOIUrl":"10.1016/j.jalgebra.2026.01.038","url":null,"abstract":"<div><div>A connected curve contained in a singular fiber of a <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-fibration is known to be contractible to a rational singular point (see <span><span>Lemma 1.1</span></span>). We are interested in characterizing some specific properties of rational singularities of this type. We also show that a proper connected curve of a relatively minimal singular fiber of a genus <span><math><mi>g</mi><mo>&gt;</mo><mn>0</mn></math></span> fibration contracts to a singularity of arithmetic genus less than <em>g</em>. In particular, for <span><math><mi>g</mi><mo>=</mo><mn>2</mn></math></span> we get either rational or elliptic singularities.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 484-496"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172054","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}

{"title":"Moving vectors and core blocks of Ariki-Koike algebras","authors":"Yanbo Li ,&nbsp;Xiangyu Qi ,&nbsp;Kai Meng Tan","doi":"10.1016/j.jalgebra.2026.01.028","DOIUrl":"10.1016/j.jalgebra.2026.01.028","url":null,"abstract":"<div><div>We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero to the graded decomposition numbers of the Iwahori-Hecke algebras of type <em>A</em>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 497-563"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172098","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}

{"title":"Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, I","authors":"Fu-Gang Yin ,&nbsp;Lei Chen","doi":"10.1016/j.jalgebra.2025.12.031","DOIUrl":"10.1016/j.jalgebra.2025.12.031","url":null,"abstract":"<div><div>In this paper, we study the primitive actions of almost simple exceptional groups of Lie type on <em>s</em>-arc-transitive digraphs. Our motivation is the following question posed by Giudici and Xia: Is there an upper bound on <em>s</em> for finite vertex-primitive <em>s</em>-arc-transitive digraphs that are not directed cycles? In a 2018 paper, Giudici and Xia reduced this question to the case where the automorphism group of the digraph is an almost simple group with socle <em>L</em>. Subsequently, it has been proved that <span><math><mi>s</mi><mo>≤</mo><mn>2</mn></math></span> when <em>L</em> is a linear, symplectic or alternating group, and <span><math><mi>s</mi><mo>≤</mo><mn>1</mn></math></span> when <em>L</em> is a Suzuki group, a small Ree group, or one of 22 specific sporadic groups. In this paper, we prove that <span><math><mi>s</mi><mo>≤</mo><mn>2</mn></math></span> when <em>L</em> is <span><math><mmultiscripts><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts><mo>(</mo><mi>q</mi><mo>)</mo></math></span>, <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span> (including <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math></span>), <span><math><mmultiscripts><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts><mo>(</mo><mi>q</mi><mo>)</mo></math></span> (including <span><math><mmultiscripts><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts><msup><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>′</mo></mrow></msup></math></span>), <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>, <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span> or <span><math><mmultiscripts><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts><mo>(</mo><mi>q</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"694 ","pages":"Pages 448-483"},"PeriodicalIF":0.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171941","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}