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Algebras and Representation Theory最新文献

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A Note on Singularity Categories and Triangular Matrix Algebras 奇异性类别和三角矩阵代数的说明
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-01-06 DOI: 10.1007/s10468-023-10249-3
Yongyun Qin
{"title":"A Note on Singularity Categories and Triangular Matrix Algebras","authors":"Yongyun Qin","doi":"10.1007/s10468-023-10249-3","DOIUrl":"10.1007/s10468-023-10249-3","url":null,"abstract":"<div><p>Let <span>(Lambda = left[ begin{array}{cc} A &amp;{} 0 M &amp;{} B end{array}right] )</span> be an Artin algebra and <span>(_BM_A)</span> a <i>B</i>-<i>A</i>-bimodule. We prove that there is a triangle equivalence <span>(D_{sg}(Lambda ) cong D_{sg}(A)coprod D_{sg}(B))</span> between the corresponding singularity categories if <span>(_BM)</span> is semi-simple and <span>(M_A)</span> is projective. As a result, we obtain a new method for describing the singularity categories of certain bounded quiver algebras.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1111 - 1119"},"PeriodicalIF":0.5,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373363","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
Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold 库兹涅佐夫-波利什丘克旋转体十倍异常集合的丰满度
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-28 DOI: 10.1007/s10468-023-10246-6
Riccardo Moschetti, Marco Rampazzo
{"title":"Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold","authors":"Riccardo Moschetti,&nbsp;Marco Rampazzo","doi":"10.1007/s10468-023-10246-6","DOIUrl":"10.1007/s10468-023-10246-6","url":null,"abstract":"<div><p>Kuznetsov and Polishchuk provided a general algorithm to construct exceptional collections of maximal length for homogeneous varieties of type <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i>. We consider the case of the spinor tenfold and we prove that the corresponding collection is full, i.e. it generates the whole derived category of coherent sheaves. We also verify strongness and purity of such collection. As a step of the proof, we construct some resolutions of homogeneous vector bundles which might be of independent interest.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1063 - 1081"},"PeriodicalIF":0.5,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139065372","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
Growth Rates of the Number of Indecomposable Summands in Tensor Powers 张量幂中不可分解求和数的增长率
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-19 DOI: 10.1007/s10468-023-10245-7
Kevin Coulembier, Victor Ostrik, Daniel Tubbenhauer
{"title":"Growth Rates of the Number of Indecomposable Summands in Tensor Powers","authors":"Kevin Coulembier,&nbsp;Victor Ostrik,&nbsp;Daniel Tubbenhauer","doi":"10.1007/s10468-023-10245-7","DOIUrl":"10.1007/s10468-023-10245-7","url":null,"abstract":"<div><p>In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related objects.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1033 - 1062"},"PeriodicalIF":0.5,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10245-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138744864","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 Gelfand–MacPherson Correspondence for Quiver Moduli 震颤模的格尔芬-麦克弗森对应关系
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-16 DOI: 10.1007/s10468-023-10248-4
Hans Franzen
{"title":"A Gelfand–MacPherson Correspondence for Quiver Moduli","authors":"Hans Franzen","doi":"10.1007/s10468-023-10248-4","DOIUrl":"10.1007/s10468-023-10248-4","url":null,"abstract":"<div><p>We show that a semi-stable moduli space of representations of an acyclic quiver can be identified with two GIT quotients by reductive groups. One of a quiver Grassmannian of a projective representation, the other of a quiver Grassmannian of an injective representation. This recovers as special cases the classical Gelfand–MacPherson correspondence and its generalization by Hu and Kim to bipartite quivers, as well as the Zelevinsky map for a quiver of Dynkin type <i>A</i> with the linear orientation.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1083 - 1110"},"PeriodicalIF":0.5,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680621","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
Classification of Orbit Closures in the Variety of 4-Dimensional Symplectic Lie Algebras 四维交点李代数中轨道闭包的分类
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-14 DOI: 10.1007/s10468-023-10244-8
Edison Alberto Fernández-Culma, Nadina Rojas
{"title":"Classification of Orbit Closures in the Variety of 4-Dimensional Symplectic Lie Algebras","authors":"Edison Alberto Fernández-Culma,&nbsp;Nadina Rojas","doi":"10.1007/s10468-023-10244-8","DOIUrl":"10.1007/s10468-023-10244-8","url":null,"abstract":"<div><p>The aim of this paper is to study the natural action of the real symplectic group, <span>({text {Sp}}(4, mathbb {R}))</span>, on the algebraic set of 4-dimensional Lie algebras admitting symplectic structures and to give a complete classification of orbit closures. We present some applications of such classification to the study of the Ricci curvature of left-invariant almost Kähler structures on four dimensional Lie groups.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1013 - 1032"},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680758","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
Quipu Quivers and Nakayama Algebras with Almost Separate Relations 具有几乎分离关系的 Quipu Quivers 和 Nakayama Algebras
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-12 DOI: 10.1007/s10468-023-10247-5
Didrik Fosse
{"title":"Quipu Quivers and Nakayama Algebras with Almost Separate Relations","authors":"Didrik Fosse","doi":"10.1007/s10468-023-10247-5","DOIUrl":"10.1007/s10468-023-10247-5","url":null,"abstract":"<div><p>A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras of quivers of a special form known as quipu quivers. Furthermore, we show how this derived equivalence can be used to produce a complete classification of linear Nakayama algebras with almost separate relations. As an application, we include a list of the derived equivalence classes of all Nakayama algebras of length <span>(le 8)</span> with almost separate relations.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"995 - 1010"},"PeriodicalIF":0.5,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10247-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574051","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
Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs Coxeter 群的反射表示和 Coxeter 图的同源性
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-07 DOI: 10.1007/s10468-023-10242-w
Hongsheng Hu
{"title":"Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs","authors":"Hongsheng Hu","doi":"10.1007/s10468-023-10242-w","DOIUrl":"10.1007/s10468-023-10242-w","url":null,"abstract":"<div><p>We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The classification is achieved by using characters of the integral homology group of certain graphs closely related to the Coxeter graph. On this basis, we also provide an explicit description of those representations on which the defining generators of the Coxeter group act by reflections.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"961 - 994"},"PeriodicalIF":0.5,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545711","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
Frobenius Kernels of Algebraic Supergroups and Steinberg’s Tensor Product Theorem 代数超群的Frobenius核与Steinberg张量积定理
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-12-04 DOI: 10.1007/s10468-023-10240-y
Taiki Shibata
{"title":"Frobenius Kernels of Algebraic Supergroups and Steinberg’s Tensor Product Theorem","authors":"Taiki Shibata","doi":"10.1007/s10468-023-10240-y","DOIUrl":"10.1007/s10468-023-10240-y","url":null,"abstract":"<div><p>For a split quasireductive supergroup <span>(mathbbm {G})</span> defined over a field, we study structure and representation of Frobenius kernels <span>(mathbbm {G}_r)</span> of <span>(mathbbm {G})</span> and we give a necessary and sufficient condition for <span>(mathbbm {G}_r)</span> to be unimodular in terms of the root system of <span>(mathbbm {G})</span>. We also establish Steinberg’s tensor product theorem for <span>(mathbbm {G})</span> under some natural assumptions.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"927 - 959"},"PeriodicalIF":0.5,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10240-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519044","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
Middle Terms of AR-sequences of Graded Kronecker Modules 分级Kronecker模ar序列的中项
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-11-29 DOI: 10.1007/s10468-023-10241-x
Jie Liu
{"title":"Middle Terms of AR-sequences of Graded Kronecker Modules","authors":"Jie Liu","doi":"10.1007/s10468-023-10241-x","DOIUrl":"10.1007/s10468-023-10241-x","url":null,"abstract":"<div><p>Let <span>((T(n),Omega ))</span> be the covering of the generalized Kronecker quiver <i>K</i>(<i>n</i>), where <span>(Omega )</span> is a bipartite orientation. Then there exists a reflection functor <span>(sigma )</span> on the category <span>({{,textrm{mod},}}(T(n),Omega ))</span>. Suppose that <span>(0rightarrow Xrightarrow Yrightarrow Zrightarrow 0)</span> is an AR-sequence in the regular component <span>(mathcal {D})</span> of <span>({{,textrm{mod},}}(T(n),Omega ))</span>, and <i>b</i>(<i>Z</i>) is the number of flow modules in the <span>(sigma )</span>-orbit of <i>Z</i>. Then the middle term <i>Y</i> is a sink (source or flow) module if and only if <span>(sigma Z)</span> is a sink (source or flow) module. Moreover, their radii and centers satisfy <span>(r(Y)=r(sigma Z)+1)</span> and <span>(C(Y)=C(sigma Z))</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"911 - 926"},"PeriodicalIF":0.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10241-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519050","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
On the Braid Group Action on Exceptional Sequences for Weighted Projective Lines 加权投影线例外序列上的辫群作用
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2023-11-23 DOI: 10.1007/s10468-023-10243-9
Edson Ribeiro Alvares, Eduardo Nascimento Marcos, Hagen Meltzer
{"title":"On the Braid Group Action on Exceptional Sequences for Weighted Projective Lines","authors":"Edson Ribeiro Alvares,&nbsp;Eduardo Nascimento Marcos,&nbsp;Hagen Meltzer","doi":"10.1007/s10468-023-10243-9","DOIUrl":"10.1007/s10468-023-10243-9","url":null,"abstract":"<div><p>We give a new and intrinsic proof of the transitivity of the braid group action on the set of full exceptional sequences of coherent sheaves on a weighted projective line. We do not use the corresponding result of Crawley-Boevey for modules over hereditary algebras. As an application we prove that the strongest global dimension of the category of coherent sheaves on a weighted projective line <span>(mathbb {X})</span> does not depend on the parameters of <span>(mathbb {X})</span>. Finally we prove that the determinant of the matrix obtained by taking the values of <i>n</i> <span>(mathbb {Z})</span>-linear functions defined on the Grothendieck group <span>(textrm{K}_0(mathbb {X}) simeq mathbb {Z}^n )</span> of the elements of a full exceptional sequence is an invariant, up to sign.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"897 - 909"},"PeriodicalIF":0.5,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519112","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
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