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Sequences of ICE-closed Subcategories via Preordered (tau ^{-1})-rigid Modules 通过预购(tau ^{-1}) -刚性模块的ice闭合子类别序列
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-07-14 DOI: 10.1007/s10468-025-10347-4
Eric J. Hanson
{"title":"Sequences of ICE-closed Subcategories via Preordered (tau ^{-1})-rigid Modules","authors":"Eric J. Hanson","doi":"10.1007/s10468-025-10347-4","DOIUrl":"10.1007/s10468-025-10347-4","url":null,"abstract":"<div><p>Let <span>(Lambda )</span> be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated <span>(Lambda )</span>-modules to classify certain (generalized) intermediate <i>t</i>-structures in the bounded derived category. We classify these “contravariantly finite ICE-sequences” using concepts from <span>(tau )</span>-tilting theory. More precisely, we introduce “cogen-preordered <span>(tau ^{-1})</span>-rigid modules” as a generalization of (the dual of) the “TF-ordered <span>(tau )</span>-rigid modules” of Mendoza and Treffinger. We then establish a bijection between the set of cogen-preordered <span>(tau ^{-1})</span>-rigid modules and certain sequences of intervals of torsion-free classes. Combined with the results of Sakai, this yields a bijection with the set of contravariantly finite ICE-sequences (of finite length), and thus also with the set of <span>((m+1))</span>-intermediate <i>t</i>-structures whose aisles are homology-determined.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"997 - 1014"},"PeriodicalIF":0.6,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10347-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929284","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
Invariants that are Covering Spaces and their Hopf Algebras 覆盖空间的不变量及其Hopf代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-07-08 DOI: 10.1007/s10468-025-10343-8
Ehud Meir
{"title":"Invariants that are Covering Spaces and their Hopf Algebras","authors":"Ehud Meir","doi":"10.1007/s10468-025-10343-8","DOIUrl":"10.1007/s10468-025-10343-8","url":null,"abstract":"<div><p>In a previous paper by the author a universal ring of invariants for algebraic structures of a given type was constructed. This ring is a polynomial algebra that is generated by certain trace diagrams. It was shown that this ring admits the structure of a rational positive self adjoint Hopf algebra (abbreviated rational PSH-algebra), and was conjectured that it always admits a lattice that is a PSH-algebra, a structure that was introduced by Zelevinsky. In this paper we solve this conjecture, showing that the universal ring of invariants splits as the tensor product of rational PSH-algebras that are either polynomial algebras in a single variable, or admit a lattice that is a PSH-algebra. We do so by considering diagrams as topological spaces, and using tools from the theory of covering spaces. As an application we derive a formula that connects Kronecker coefficients with finite index subgroups of free groups and representations of their Weyl groups, and a formula for the number of conjugacy classes of finite index subgroup in a finitely generated group that admits a surjective homomorphism onto the group of integers.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"883 - 920"},"PeriodicalIF":0.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10343-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929288","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
Symmetries of Quiver Schemes 颤振方案的对称性
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-06-25 DOI: 10.1007/s10468-025-10340-x
Ryo Terada, Daisuke Yamakawa
{"title":"Symmetries of Quiver Schemes","authors":"Ryo Terada,&nbsp;Daisuke Yamakawa","doi":"10.1007/s10468-025-10340-x","DOIUrl":"10.1007/s10468-025-10340-x","url":null,"abstract":"<div><p>We introduce reflection functors on quiver schemes in the sense of Hausel–Wong–Wyss, generalizing those on quiver varieties. Also we construct some isomorphisms between quiver schemes whose underlying quivers are different.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"841 - 871"},"PeriodicalIF":0.6,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169111","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
Categorifications of Non-Integer Quivers: Type ( {I_2(2n)}) 非整数箭囊的分类：类型 ( {I_2(2n)})
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-06-17 DOI: 10.1007/s10468-025-10338-5
Drew Damien Duffield, Pavel Tumarkin
{"title":"Categorifications of Non-Integer Quivers: Type ( {I_2(2n)})","authors":"Drew Damien Duffield,&nbsp;Pavel Tumarkin","doi":"10.1007/s10468-025-10338-5","DOIUrl":"10.1007/s10468-025-10338-5","url":null,"abstract":"<div><p>We use weighted unfoldings of quivers to provide a categorification of mutations of quivers of types <span>( I_2(2n) )</span>, thus extending the construction of categorifications of mutations of quivers to all finite types.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"787 - 840"},"PeriodicalIF":0.6,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10338-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166997","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 Gluing Cosilting Objects 关于粘合粘合物体的注意事项
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-06-11 DOI: 10.1007/s10468-025-10344-7
Yongliang Sun, Yaohua Zhang
{"title":"A Note on Gluing Cosilting Objects","authors":"Yongliang Sun,&nbsp;Yaohua Zhang","doi":"10.1007/s10468-025-10344-7","DOIUrl":"10.1007/s10468-025-10344-7","url":null,"abstract":"<div><p>Based on the recent works of M. Saorín and A. Zvonoreva on gluing (co)silting objects and of L. Angeler Hügel, R. Laking, J. S̆t̆ovíc̆ek and J. Vitória on mutating (co)silting objects, we first study further on gluing pure-injective cosilting objects in algebraically compactly generated triangulated categories and gluing cosilting complexes in the derived categories of rings. Then we discuss the compatibility of cosilting gluing and cosilting mutation.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"767 - 785"},"PeriodicalIF":0.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163971","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
Holonomic ( Amathcal {V})-Modules for the Affine Space 完整的( Amathcal {V}) -仿射空间的模块
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-06-09 DOI: 10.1007/s10468-025-10342-9
Yuly Billig, Henrique Rocha
{"title":"Holonomic ( Amathcal {V})-Modules for the Affine Space","authors":"Yuly Billig,&nbsp;Henrique Rocha","doi":"10.1007/s10468-025-10342-9","DOIUrl":"10.1007/s10468-025-10342-9","url":null,"abstract":"<div><p>We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein inequality for these representations, enabling us to focus on modules with minimal growth, known as holonomic modules. We show that simple holonomic modules are isomorphic to the tensor product of a holonomic module over the Weyl algebra and a finite-dimensional <span>( mathfrak {gl}_n )</span>-module. We also prove that holonomic modules have a finite length and that the representation map associated with a holonomic module is a differential operator. Finally, we present examples illustrating our results.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"755 - 766"},"PeriodicalIF":0.6,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163986","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
Building Pretorsion Theories from Torsion Theories 从扭转理论建立预扭转理论
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-05-22 DOI: 10.1007/s10468-025-10337-6
Federico Campanini, Francesca Fedele
{"title":"Building Pretorsion Theories from Torsion Theories","authors":"Federico Campanini,&nbsp;Francesca Fedele","doi":"10.1007/s10468-025-10337-6","DOIUrl":"10.1007/s10468-025-10337-6","url":null,"abstract":"<div><p>Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theories, the definition has been extended to general (non-pointed) categories. Many examples have been investigated in several different contexts, such as topological spaces and topological groups, internal preorders, preordered groups, toposes, V-groups, crossed modules, etc. In this paper, we show that pretorsion theories naturally appear also in the “classical” framework, namely in abelian categories. We propose two ways of obtaining pretorsion theories starting from torsion theories. The first one uses “comparable” torsion theories, while the second one extends a torsion theory with a Serre subcategory. We also give a universal way of obtaining a torsion theory from a given pretorsion theory in additive categories. We conclude by providing several examples in module categories, internal groupoids, recollements and representation theory.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"737 - 753"},"PeriodicalIF":0.6,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10337-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168583","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
From Green’s Formula to Derived Hall Algebras 从格林公式到派生的霍尔代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-05-17 DOI: 10.1007/s10468-025-10335-8
Ji Lin
{"title":"From Green’s Formula to Derived Hall Algebras","authors":"Ji Lin","doi":"10.1007/s10468-025-10335-8","DOIUrl":"10.1007/s10468-025-10335-8","url":null,"abstract":"<div><p>The aim of this note is to clarify the relationship between Green’s formula and the associativity of multiplication for derived Hall algebra in the sense of Toën (Duke Math J 135(3):587-615, 2006), Xiao and Xu (Duke Math J 143(2):357-373, 2008) and Xu and Chen (Algebr Represent Theory 16(3):673-687, 2013). Let <span>(mathcal {A})</span> be a finitary hereditary abelian category. It is known that the associativity of the derived Hall algebra <span>(mathcal {D}mathcal {H}_t(mathcal {A}))</span> implies Green’s formula. We introduce a new algebra <span>({mathcal {L}}_t({mathcal {A}}))</span> whose associativity is deduced from Green’s formula, and show that it is isomorphic to the derived Hall algebra <span>(mathcal {D}mathcal {H}_t(mathcal {A}))</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"709 - 735"},"PeriodicalIF":0.6,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166979","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
Correction: Universal Quantum (semi)groups and Hopf Envelopes: Erratum 更正：通用量子（半）群和霍普夫包络：勘误
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-05-16 DOI: 10.1007/s10468-025-10329-6
Marco Andrés Farinati
{"title":"Correction: Universal Quantum (semi)groups and Hopf Envelopes: Erratum","authors":"Marco Andrés Farinati","doi":"10.1007/s10468-025-10329-6","DOIUrl":"10.1007/s10468-025-10329-6","url":null,"abstract":"","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 3","pages":"873 - 881"},"PeriodicalIF":0.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166552","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
Demazure Filtration of Tensor Product Modules of Current Lie Algebra of Type (A_1) 一类当前李代数张量积模的变形滤波 (A_1)
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2025-04-29 DOI: 10.1007/s10468-025-10334-9
Divya Setia, Tanusree Khandai
{"title":"Demazure Filtration of Tensor Product Modules of Current Lie Algebra of Type (A_1)","authors":"Divya Setia,&nbsp;Tanusree Khandai","doi":"10.1007/s10468-025-10334-9","DOIUrl":"10.1007/s10468-025-10334-9","url":null,"abstract":"<div><p>In this paper we study the structure of finite-dimensional representations of the current Lie algebra of type <span>(A_1)</span>, <span>(mathfrak {sl}_2[t])</span>, which are obtained by taking tensor products of local Weyl modules with Demazure modules. We show that such a representation admits a Demazure flag and obtain a closed formula for the graded multiplicities of the level 2 Demazure modules in the filtration of the tensor product of two local Weyl modules for <span>(mathfrak {sl}_2[t])</span>. Furthermore, we show that the tensor product of a local Weyl module with an irreducible <span>(mathfrak {sl}_2[t])</span> module admits a Demazure filtration and derive the graded character of such tensor product modules. In conjunction with the results of Chari et al. (SIGMA Symmetry Integrability Geom. Methods Appl. <b>10</b>(032), 2014), our findings provide evidence for the conjecture in Blanton (2017) that the tensor product of Demazure modules of levels m and n respectively has a filtration by Demazure modules of level m + n.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 2","pages":"679 - 707"},"PeriodicalIF":0.5,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100238","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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