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Algebras and Representation Theory最新文献

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Preradicals Over Some Group Algebras 某些群代数上的悖论
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-01-25 DOI: 10.1007/s10468-024-10256-y
Rogelio Fernández-Alonso, Benigno Mercado, Silvia Gavito
{"title":"Preradicals Over Some Group Algebras","authors":"Rogelio Fernández-Alonso,&nbsp;Benigno Mercado,&nbsp;Silvia Gavito","doi":"10.1007/s10468-024-10256-y","DOIUrl":"10.1007/s10468-024-10256-y","url":null,"abstract":"<div><p>For a field <span>(varvec{K})</span> and a finite group <span>(varvec{G})</span>, we study the lattice of preradicals over the group algebra <span>(varvec{KG})</span>, denoted by <span>(varvec{KG})</span>-<span>(varvec{pr})</span>. We show that if <span>(varvec{KG})</span> is a semisimple algebra, then <span>(varvec{KG})</span>-<span>(varvec{pr})</span> is completely described, and we establish conditions for counting the number of its atoms in some specific cases. If <span>(varvec{KG})</span> is an algebra of finite representation type, but not a semisimple one, we completely describe <span>(varvec{KG})</span>-<span>(varvec{pr})</span> when the characteristic of <span>(varvec{K})</span> is a prime <span>(varvec{p})</span> and <span>(varvec{G})</span> is a cyclic <span>(varvec{p})</span>-group. For group algebras of infinite representation type, we show that the lattices of preradicals over two representative families of such algebras are not sets (in which case, we say the algebras are <span>(varvec{mathfrak {p}})</span>-large). Besides, we provide new examples of <span>(varvec{mathfrak {p}})</span>-large algebras. Finally, we prove the main theorem of this paper which characterizes the representation type of group algebras <span>(varvec{KG})</span> in terms of their lattice of preradicals.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1221 - 1235"},"PeriodicalIF":0.5,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587328","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
Publisher Correction: Quipu Quivers and Nakayama Algebras with Almost Separate Relations 出版商更正：具有几乎独立关系的奎布四元组和中山代数
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-01-25 DOI: 10.1007/s10468-024-10252-2
Didrik Fosse
{"title":"Publisher Correction: Quipu Quivers and Nakayama Algebras with Almost Separate Relations","authors":"Didrik Fosse","doi":"10.1007/s10468-024-10252-2","DOIUrl":"10.1007/s10468-024-10252-2","url":null,"abstract":"","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"1011 - 1011"},"PeriodicalIF":0.5,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10252-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413572","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 Quantization of the Loday-Ronco Hopf Algebra Loday-Ronco 霍普夫代数的量子化
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-01-20 DOI: 10.1007/s10468-024-10253-1
João N. Esteves
{"title":"A Quantization of the Loday-Ronco Hopf Algebra","authors":"João N. Esteves","doi":"10.1007/s10468-024-10253-1","DOIUrl":"10.1007/s10468-024-10253-1","url":null,"abstract":"<div><p>We propose a quantization algebra of the Loday-Ronco Hopf algebra <span>(k[Y^infty ])</span>, based on the Topological Recursion formula of Eynard and Orantin. We have shown in previous works that the Loday-Ronco Hopf algebra of planar binary trees is a space of solutions for the genus 0 version of Topological Recursion, and that an extension of the Loday Ronco Hopf algebra as to include some new graphs with loops is the correct setting to find a solution space for arbitrary genus. Here we show that this new algebra <span>(k[Y^infty ]_h)</span> is still a Hopf algebra that can be seen in some sense to be made precise in the text as a quantization of the Hopf algebra of planar binary trees, and that the solution space of Topological Recursion <span>(mathcal {A}^h_{text {TopRec}})</span> is a subalgebra of a quotient algebra <span>(mathcal {A}_{text {Reg}}^h)</span> obtained from <span>(k[Y^infty ]_h)</span> that nevertheless doesn’t inherit the Hopf algebra structure. We end the paper with a discussion on the cohomology of <span>(mathcal {A}^h_{text {TopRec}})</span> in low degree.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1177 - 1201"},"PeriodicalIF":0.5,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10253-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509411","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
Minimal Triangular Structures on Abelian Extensions 阿贝尔扩展上的最小三角形结构
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-01-12 DOI: 10.1007/s10468-023-10250-w
Hong Fei Zhang, Kun Zhou
{"title":"Minimal Triangular Structures on Abelian Extensions","authors":"Hong Fei Zhang,&nbsp;Kun Zhou","doi":"10.1007/s10468-023-10250-w","DOIUrl":"10.1007/s10468-023-10250-w","url":null,"abstract":"<div><p>We study minimal triangular structures on abelian extensions. In particular, we construct a family of minimal triangular semisimple Hopf algebras and prove that the Hopf algebra <span>(H_{b:y})</span> in the semisimple Hopf algebras of dimension 16 classified by Y. Kashina in 2000 is minimal triangular Hopf algebra with smallest dimension among non-trivial semisimple triangular Hopf algebras (i.e. not group algebras or their dual).</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1121 - 1136"},"PeriodicalIF":0.5,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139465152","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
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
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