Journal of the London Mathematical Society-Second Series最新文献

Asymptotic estimates of large gaps between directions in certain planar quasicrystals 某些平面准晶体方向间大间隙的渐近估计

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-30 DOI: 10.1112/jlms.70187

Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu

{"title":"Asymptotic estimates of large gaps between directions in certain planar quasicrystals","authors":"Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu","doi":"10.1112/jlms.70187","DOIUrl":"https://doi.org/10.1112/jlms.70187","url":null,"abstract":"For quasicrystals of cut-and-project type in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>SL</mo>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$operatorname{SL}_d(mathbb {R})$</annotation>\u0000 </semantics></math>-invariant point processes. In this paper, we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70187","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144172000","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

One-dimensional Carrollian fluids III: Global existence and weak continuity in L ∞ $L^infty$ 一维Carrollian流体III: L∞上的整体存在性和弱连续性 $L^infty$

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-30 DOI: 10.1112/jlms.70186

Marios Petropoulos, Simon Schulz, Grigalius Taujanskas

{"title":"One-dimensional Carrollian fluids III: Global existence and weak continuity in \u0000 \u0000 \u0000 L\u0000 ∞\u0000 \u0000 $L^infty$","authors":"Marios Petropoulos, Simon Schulz, Grigalius Taujanskas","doi":"10.1112/jlms.70186","DOIUrl":"https://doi.org/10.1112/jlms.70186","url":null,"abstract":"The Carrollian fluid equations arise as the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>c</mi>\u0000 <mo>→</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$c rightarrow 0$</annotation>\u0000 </semantics></math> limit of the relativistic fluid equations and have recently experienced a surge of activity in the flat-space holography community. However, the rigorous mathematical well-posedness theory for these equations does not appear to have been previously studied. This paper is the third in a series in which we initiate the systematic analysis of the Carrollian fluid equations. In the present work, we prove the global-in-time existence of bounded entropy solutions to the isentropic Carrollian fluid equations in one spatial dimension for a particular constitutive law (<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$gamma = 3$</annotation>\u0000 </semantics></math>). Our method is to use a vanishing viscosity approximation for which we establish a compensated compactness framework. Using this framework we also prove the compactness of entropy solutions in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math>, and establish a kinetic formulation of the problem. This global existence result in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> extends the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$C^1$</annotation>\u0000 </semantics></math> theory presented in [2].","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144172002","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

Cyclic branched covers of Seifert links and properties related to the A D E $ADE$ link conjecture Seifert链的循环分支盖及与ADE$ ADE$链猜想有关的性质

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-30 DOI: 10.1112/jlms.70178

Steven Boyer, Cameron McA. Gordon, Ying Hu

{"title":"Cyclic branched covers of Seifert links and properties related to the \u0000 \u0000 \u0000 A\u0000 D\u0000 E\u0000 \u0000 $ADE$\u0000 link conjecture","authors":"Steven Boyer, Cameron McA. Gordon, Ying Hu","doi":"10.1112/jlms.70178","DOIUrl":"https://doi.org/10.1112/jlms.70178","url":null,"abstract":"In this article, we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-spaces, if and only if it is not an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>D</mi>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$ADE$</annotation>\u0000 </semantics></math> link up to orientation. This leads to a proof of the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>D</mi>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$ADE$</annotation>\u0000 </semantics></math> link conjecture for Seifert links. When <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>D</mi>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$ADE$</annotation>\u0000 </semantics></math> link up to orientation, we determine which of its canonical <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-fold cyclic branched covers <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Σ</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>L</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Sigma _n(L)$</annotation>\u0000 </semantics></math> have nonleft-orderable fundamental groups. In addition, we give a topological proof of Ishikawa's classification of strongly quasi-positive Seifert links and we determine the Seifert links that are definite, resp., have genus zero, resp. have genus equal to its smooth 4-ball genus, among others. In the last section, we provide a comprehensive survey of the current knowledge and results concerning the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>D</mi>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$ADE$</annotation>\u0000 </semantics></math> link conjecture.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70178","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144172003","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

Wall-crossing for quasimaps to GIT stack bundles 准映射到GIT堆栈包的跨墙

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-29 DOI: 10.1112/jlms.70185

Shidhesh Supekar, Hsian-Hua Tseng

引用次数: 0

A granular model for crowd motion and pedestrian flow 人群运动和行人流的颗粒模型

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-26 DOI: 10.1112/jlms.70184

Noureddine Igbida, José Miguel Urbano

引用次数: 0

Hypersonic flow onto a large curved wedge and the dissipation of shock wave 高超声速大弯曲楔流与激波耗散

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-26 DOI: 10.1112/jlms.70182

Dian Hu, Aifang Qu

{"title":"Hypersonic flow onto a large curved wedge and the dissipation of shock wave","authors":"Dian Hu, Aifang Qu","doi":"10.1112/jlms.70182","DOIUrl":"https://doi.org/10.1112/jlms.70182","url":null,"abstract":"The flow field with a Mach number larger than 5 is named hypersonic flow. In this paper, we explore the existence of smooth flow field after shock for hypersonic potential flow past a curved smooth wedge with neither smallness assumption on the height of the wedge nor that it is a bounded variation (BV) perturbation of a line. The asymptotic behaviour of the shock is also analysed. We prove that for a given Bernoulli constant of the incoming flow, there exists a sufficient large constant such that if the Mach number of the incoming flow is larger than it, then there exists a global shock wave attached to the tip of the wedge together with a smooth flow field between it and the wedge. The state of the flow after shock is in a neighbourhood of a curve that is determined by the wedge and the density of the incoming flow. If the slope of the wedge has a positive limit as <math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> goes to infinity, then the slope of the shock tends to that of the self-similar case that the same incoming flow past a straight wedge with slope of the limit. Specifically, we demonstrate that if the slope of the wedge is parallel to the incoming flow at infinity, the strength of the shock will diminish to zero at infinity. The restrictions on the surface of a wedge have been greatly relaxed compared to the previous works on supersonic flow past wedges. The method employed in this paper is characteristic decomposition, and the existence of the solution is obtained by finding an invariant domain of the solution based on geometry structures of the governing equations. The ideas and methods presented here may be applicable to other problems.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140776","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

Categorifying non-commutative deformations 分类非交换变形

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-26 DOI: 10.1112/jlms.70176

Agnieszka Bodzenta, Alexey Bondal

{"title":"Categorifying non-commutative deformations","authors":"Agnieszka Bodzenta, Alexey Bondal","doi":"10.1112/jlms.70176","DOIUrl":"https://doi.org/10.1112/jlms.70176","url":null,"abstract":"We define the functor <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ncDef</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>Z</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>Z</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$textrm {ncDef}_{(Z_1,ldots ,Z_n)}$</annotation>\u0000 </semantics></math> of non-commutative deformations of an <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-tuple of objects in an arbitrary <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$mathbb {k}$</annotation>\u0000 </semantics></math>-linear abelian category <math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$mathcal {Z}$</annotation>\u0000 </semantics></math>. In our categorified approach, we view the underlying spaces of infinitesimal flat deformations as Deligne finite categories, that is, finite length abelian categories admitting projective generators, with <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> isomorphism classes of simple objects. More generally, we define the functor <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ncDef</mi>\u0000 <mi>ζ</mi>\u0000 </msub>\u0000 <annotation>$textrm {ncDef}_{zeta }$</annotation>\u0000 </semantics></math> of non-commutative deformations of an exact functor <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ζ</mi>\u0000 <mo>:</mo>\u0000 <mi>A</mi>\u0000 <mo>→</mo>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$zeta colon mathcal {A} rightarrow mathcal {Z}$</annotation>\u0000 </semantics></math> of abelian categories. Here the role of an infinitesimal non-commutative thickening of <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>${mathcal {A}}$</annotation>\u0000 </semantics></math> is played by an abelian category <math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>${mathcal {B}}$</annotation>\u0000 </semantics></math> containing <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>${mathcal {A}}$</annotation>\u0000 </semantics></math> and such that <math>\u0000","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140352","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

C R $CR$ analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension 利用局部一致补全、锐极大模原理和全纯扩展分析CR$ CR$

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-26 DOI: 10.1112/jlms.70135

Mauro Nacinovich, Egmont Porten

{"title":"C\u0000 R\u0000 \u0000 $CR$\u0000 analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension","authors":"Mauro Nacinovich, Egmont Porten","doi":"10.1112/jlms.70135","DOIUrl":"https://doi.org/10.1112/jlms.70135","url":null,"abstract":"Using iterated uniform local completion, we introduce a notion of continuous <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> functions on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> submanifolds. Under additional assumptions of set-theoretical weak pseudo-concavity, we prove optimal maximum modulus principles for these functions, extending classical results for holomorphic functions and ordinary <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> functions. Restricting to real submanifolds (possibly with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> singularities) of complex manifolds, we generalise results on holomorphic extension to full neighbourhoods known before only for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> submanifolds. The article is concluded by a study of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$CR$</annotation>\u0000 </semantics></math> singularities and explicit constructions of submanifolds on which the extension results are valid.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140775","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

Entire curves generating all shapes of Nevanlinna currents 整个曲线产生了各种形状的奈凡林纳电流

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-25 DOI: 10.1112/jlms.70177

Hao Wu, Song-Yan Xie

{"title":"Entire curves generating all shapes of Nevanlinna currents","authors":"Hao Wu, Song-Yan Xie","doi":"10.1112/jlms.70177","DOIUrl":"https://doi.org/10.1112/jlms.70177","url":null,"abstract":"First, we show that every complex torus <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$mathbb {T}$</annotation>\u0000 </semantics></math> contains some entire curve <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>:</mo>\u0000 <mi>C</mi>\u0000 <mo>→</mo>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <annotation>$g: mathbb {C}rightarrow mathbb {T}$</annotation>\u0000 </semantics></math> such that the concentric holomorphic discs <math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mi>g</mi>\u0000 <mspace></mspace>\u0000 <msub>\u0000 <mo>|</mo>\u0000 <msub>\u0000 <mover>\u0000 <mi>D</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mi>r</mi>\u0000 </msub>\u0000 </msub>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$lbrace g,vert _{overline{mathbb {D}}_{r}}rbrace _{r>0}$</annotation>\u0000 </semantics></math> can generate all the Nevanlinna/Ahlfors currents on <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$mathbb {T}$</annotation>\u0000 </semantics></math> at cohomological level. This confirms an anticipation of Sibony. Developing further our new method, we can construct some twisted entire curve <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>C</mi>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>CP</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$f: mathbb {C}rightarrow mathbb {CP}^1times E$</annotation>\u0000 </semantics></math> in the product of the rational curve <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>CP</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$mathbb {CP}^1$</annotation>\u0000 </semantics></math> and an elliptic curve <math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math>, such that, concerning Siu's decomposition, demanding any cardinality <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135781","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

The Temperley–Lieb tower and the Weyl algebra 坦波利-利布塔和魏尔代数

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-25 DOI: 10.1112/jlms.70174

Matthew Harper, Peter Samuelson

{"title":"The Temperley–Lieb tower and the Weyl algebra","authors":"Matthew Harper, Peter Samuelson","doi":"10.1112/jlms.70174","DOIUrl":"https://doi.org/10.1112/jlms.70174","url":null,"abstract":"We define a monoidal category <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>${mathbf {W}}$</annotation>\u0000 </semantics></math> and a closely related 2-category <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>Weyl</mi>\u0000 </mrow>\u0000 <annotation>${mathbf {2Weyl}}$</annotation>\u0000 </semantics></math> using diagrammatic methods. We show that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>Weyl</mi>\u0000 </mrow>\u0000 <annotation>${mathbf {2Weyl}}$</annotation>\u0000 </semantics></math> acts on the category <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>TL</mi>\u0000 <mo>:</mo>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mo>⨁</mo>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <msub>\u0000 <mo>TL</mo>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>−</mo>\u0000 <mi>mod</mi>\u0000 </mrow>\u0000 <annotation>$mathbf {TL}:=bigoplus _n operatorname{TL}_nmathrm{-mod}$</annotation>\u0000 </semantics></math> of modules over Temperley–Lieb algebras, with its generating 1-morphisms acting by induction and restriction. The Grothendieck groups of <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>${mathbf {W}}$</annotation>\u0000 </semantics></math> and a third category we define <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>${mathbf {W}}^infty$</annotation>\u0000 </semantics></math> are closely related to the Weyl algebra. We formulate a sense in which <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$K_0({mathbf {W}}^infty)$</annotation>\u0000 </semantics></math> acts asymptotically on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135779","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