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Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams 由具有 3 阶轨道点的曲面产生的温和代数，第一部分：散射图
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-29 DOI: 10.1007/s10468-023-10233-x
Daniel Labardini-Fragoso, Lang Mou
{"title":"Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams","authors":"Daniel Labardini-Fragoso,&nbsp;Lang Mou","doi":"10.1007/s10468-023-10233-x","DOIUrl":"10.1007/s10468-023-10233-x","url":null,"abstract":"<div><p>To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability scattering diagrams of such gentle algebras and use them to prove that the Caldero–Chapoton map defines a bijection between <span>(tau )</span>-rigid pairs and cluster monomials of the generalized cluster algebra associated to the surface by Chekhov and Shapiro.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"679 - 722"},"PeriodicalIF":0.5,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10233-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135199595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Note on the Global Dimension of Shifted Orders 关于订单转移的全球层面的说明
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-22 DOI: 10.1007/s10468-023-10229-7
Özgür Esentepe
{"title":"A Note on the Global Dimension of Shifted Orders","authors":"Özgür Esentepe","doi":"10.1007/s10468-023-10229-7","DOIUrl":"10.1007/s10468-023-10229-7","url":null,"abstract":"<div><p>We consider the dominant dimension of an order over a Cohen-Macaulay ring in the category of centrally Cohen-Macaulay modules. There is a canonical tilting module in the case of positive dominant dimension and we give an upper bound on the global dimension of its endomorphism ring.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"667 - 678"},"PeriodicalIF":0.5,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10229-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136010807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants Dessins D'Enfants、Brauer Graph Algebras 和 Galois Invariants
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-18 DOI: 10.1007/s10468-023-10232-y
Goran Malić, Sibylle Schroll
{"title":"Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants","authors":"Goran Malić,&nbsp;Sibylle Schroll","doi":"10.1007/s10468-023-10232-y","DOIUrl":"10.1007/s10468-023-10232-y","url":null,"abstract":"<div><p>In this paper, we associate a finite dimensional algebra, called a Brauer graph algebra, to every clean dessin d’enfant by constructing a quiver based on the monodromy of the dessin. We show that Galois conjugate dessins d’enfants give rise to derived equivalent Brauer graph algebras and that the stable Auslander-Reiten quiver and the dimension of the Brauer graph algebra are invariant under the induced action of the absolute Galois group.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"655 - 665"},"PeriodicalIF":0.5,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10232-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135110702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Gorenstein Rings via Homological Dimensions, and Symmetry in Vanishing of Ext and Tate Cohomology 通过同调维的Gorenstein环，以及Ext和Tate上同调消失的对称性
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-15 DOI: 10.1007/s10468-023-10223-z
Dipankar Ghosh, Tony J. Puthenpurakal
{"title":"Gorenstein Rings via Homological Dimensions, and Symmetry in Vanishing of Ext and Tate Cohomology","authors":"Dipankar Ghosh,&nbsp;Tony J. Puthenpurakal","doi":"10.1007/s10468-023-10223-z","DOIUrl":"10.1007/s10468-023-10223-z","url":null,"abstract":"<div><p>The aim of this article is to consider the spectral sequences induced by tensor-hom adjunction, and provide a number of new results. Let <i>R</i> be a commutative Noetherian local ring of dimension <i>d</i>. In the 1st part, it is proved that <i>R</i> is Gorenstein if and only if it admits a nonzero CM (Cohen-Macaulay) module <i>M</i> of finite Gorenstein dimension <i>g</i> such that <span>(text {type}(M) leqslant mu ( text {Ext}_R^g(M,R) ))</span> (e.g., <span>(text {type}(M)=1)</span>). This considerably strengthens a result of Takahashi. Moreover, we show that if there is a nonzero <i>R</i>-module <i>M</i> of depth <span>(geqslant d - 1)</span> such that the injective dimensions of <i>M</i>, <span>(text {Hom}_R(M,M))</span> and <span>(text {Ext}_R^1(M,M))</span> are finite, then <i>M</i> has finite projective dimension and <i>R</i> is Gorenstein. In the 2nd part, we assume that <i>R</i> is CM with a canonical module <span>(omega )</span>. For CM <i>R</i>-modules <i>M</i> and <i>N</i>, we show that the vanishing of one of the following implies the same for others: <span>(text {Ext}_R^{gg 0}(M,N^{+}))</span>, <span>(text {Ext}_R^{gg 0}(N,M^{+}))</span> and <span>(text {Tor}_{gg 0}^R(M,N))</span>, where <span>(M^{+})</span> denotes <span>(text {Ext}_R^{d-dim (M)}(M,omega ))</span>. This strengthens a result of Huneke and Jorgensen. Furthermore, we prove a similar result for Tate cohomologies under the additional condition that <i>R</i> is Gorenstein.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"639 - 653"},"PeriodicalIF":0.5,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49216046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Extremal Tensor Products of Demazure Crystals 德马祖尔晶体的极值张量乘积
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-12 DOI: 10.1007/s10468-023-10231-z
Sami Assaf, Anne Dranowski, Nicolle González
{"title":"Extremal Tensor Products of Demazure Crystals","authors":"Sami Assaf,&nbsp;Anne Dranowski,&nbsp;Nicolle González","doi":"10.1007/s10468-023-10231-z","DOIUrl":"10.1007/s10468-023-10231-z","url":null,"abstract":"<div><p>Demazure crystals are subcrystals of highest weight irreducible <span>(mathfrak {g})</span>-crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when the tensor product of Demazure crystals is extremal. We then show that tensor products of Demazure crystals decompose into direct sums of Demazure crystals if and only if the tensor product is extremal, thus providing a sufficient and necessary local criterion for when the tensor product of Demazure crystals is itself Demazure. As an application, we show that the primary component in the tensor square of any Demazure crystal is always Demazure.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"627 - 638"},"PeriodicalIF":0.5,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10231-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135878205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Onset of Regularity for FI-modules FI 模块的正则性开始
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-12 DOI: 10.1007/s10468-023-10228-8
Cihan Bahran
{"title":"Onset of Regularity for FI-modules","authors":"Cihan Bahran","doi":"10.1007/s10468-023-10228-8","DOIUrl":"10.1007/s10468-023-10228-8","url":null,"abstract":"<div><p>In terms of local cohomology, we give an explicit range as to when the <b>FI</b>-homology of an <b>FI</b>-module attains the degree predicted by its regularity.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"613 - 625"},"PeriodicalIF":0.5,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135878221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Auto-Correlation Functions for Unitary Groups 单元群的自相关函数
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-11 DOI: 10.1007/s10468-023-10225-x
Kyu-Hwan Lee, Se-Jin Oh
{"title":"Auto-Correlation Functions for Unitary Groups","authors":"Kyu-Hwan Lee,&nbsp;Se-Jin Oh","doi":"10.1007/s10468-023-10225-x","DOIUrl":"10.1007/s10468-023-10225-x","url":null,"abstract":"<div><p>We compute the auto-correlations functions of order <span>(mge 1)</span> for the characteristic polynomials of random matrices from certain subgroups of the unitary groups <span>({text {U}}(2))</span> and <span>({text {U}}(3))</span> by establishing new branching rules. These subgroups can be understood as certain analogues of Sato–Tate groups of <span>({text {USp}}(4))</span> in our previous paper. Our computation yields symmetric polynomial identities with <i>m</i>-variables involving irreducible characters of <span>({text {U}}(m))</span> for all <span>(m ge 1)</span> in an explicit, uniform way.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"583 - 611"},"PeriodicalIF":0.5,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dimer Algebras, Ghor Algebras, and Cyclic Contractions 二聚体代数、古尔代数和循环收缩
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-07 DOI: 10.1007/s10468-023-10224-y
Charlie Beil
{"title":"Dimer Algebras, Ghor Algebras, and Cyclic Contractions","authors":"Charlie Beil","doi":"10.1007/s10468-023-10224-y","DOIUrl":"10.1007/s10468-023-10224-y","url":null,"abstract":"<div><p>A ghor algebra is the path algebra of a dimer quiver on a surface, modulo relations that come from the perfect matchings of its quiver. Such algebras arise from abelian quiver gauge theories in physics. We show that a ghor algebra <span>(Lambda )</span> on a torus is a dimer algebra (a quiver with potential) if and only if it is noetherian, and otherwise <span>(Lambda )</span> is the quotient of a dimer algebra by homotopy relations. Furthermore, we classify the simple <span>(Lambda )</span>-modules of maximal dimension and give an explicit description of the center of <span>(Lambda )</span> using a special subset of perfect matchings. In our proofs we introduce formalized notions of Higgsing and the mesonic chiral ring from quiver gauge theory.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"547 - 582"},"PeriodicalIF":0.5,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10224-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52368933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An Indicator Formula for the Hopf Algebra (k^{S_{n-1}}#kC_n) Hopf代数的一个指标公式 $$k^{S_{n-1}}#kC_n$$
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-09-06 DOI: 10.1007/s10468-023-10230-0
Kayla Orlinsky
{"title":"An Indicator Formula for the Hopf Algebra (k^{S_{n-1}}#kC_n)","authors":"Kayla Orlinsky","doi":"10.1007/s10468-023-10230-0","DOIUrl":"10.1007/s10468-023-10230-0","url":null,"abstract":"<div><p>The semisimple bismash product Hopf algebra <span>(J_n=k^{S_{n-1}}#kC_n)</span> for an algebraically closed field <i>k</i> is constructed using the matched pair actions of <span>(C_n)</span> and <span>(S_{n-1})</span> on each other. In this work, we reinterpret these actions and use an understanding of the involutions of <span>(S_{n-1})</span> to derive a new Froebnius-Schur indicator formula for irreps of <span>(J_n)</span> and show that for <i>n</i> odd, all indicators of <span>(J_n)</span> are nonnegative. We also derive a variety of counting formulas including Theorem 6.2.2 which fully describes the indicators of all 2-dimensional irreps of <span>(J_n)</span> and Theorem 6.1.2 which fully describes the indicators of all odd-dimensional irreps of <span>(J_n)</span> and use these formulas to show that nonzero indicators become rare for large <i>n</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"495 - 545"},"PeriodicalIF":0.5,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10230-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44116669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Drinfeld-Type Presentation of the Orthosymplectic Yangians 正辛杨岩系的旱田型表现
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-08-18 DOI: 10.1007/s10468-023-10227-9
A. I. Molev
{"title":"A Drinfeld-Type Presentation of the Orthosymplectic Yangians","authors":"A. I. Molev","doi":"10.1007/s10468-023-10227-9","DOIUrl":"10.1007/s10468-023-10227-9","url":null,"abstract":"<div><p>We use the Gauss decomposition of the generator matrix in the <i>R</i>-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra <span>(mathfrak {osp}_{N|2m})</span> to produce its Drinfeld-type presentation. The results rely on a super-version of the embedding theorem which allows one to identify a subalgebra in the <i>R</i>-matrix presentation which is isomorphic to the Yangian associated with <span>(mathfrak {osp}_{N|2m-2})</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"469 - 494"},"PeriodicalIF":0.5,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10227-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45744008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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