Algebras and Representation Theory最新文献_第2页

Some Universal Constructions in Representation Theory 表征理论中的一些普遍构造

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2024-07-31 DOI: 10.1007/s10468-024-10278-6

Claudio Procesi

引用次数: 0

Weak Silting Modules 弱淤积模块

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-07-27 DOI: 10.1007/s10468-024-10276-8

Qianqian Yuan, Hailou Yao

引用次数: 0

Butler’s Method Applied to (mathbb {Z}_p[C_ptimes C_p])-Permutation Modules 巴特勒方法应用于 $$mathbb {Z}_p[C_ptimes C_p]$$ -Permutation 模块

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-07-22 DOI: 10.1007/s10468-024-10277-7

John W. MacQuarrie, Marlon Estanislau

{"title":"Butler’s Method Applied to (mathbb {Z}_p[C_ptimes C_p])-Permutation Modules","authors":"John W. MacQuarrie, Marlon Estanislau","doi":"10.1007/s10468-024-10277-7","DOIUrl":"10.1007/s10468-024-10277-7","url":null,"abstract":"<div>Let G be a finite p-group with normal subgroup (varvec{N}) of order (varvec{p}). The first author and Zalesskii have previously shown that a (mathbb {Z}_p) (varvec{G})-lattice is a permutation module if, and only if, its (varvec{N})-invariants, its (varvec{N})-coinvariants, and a third module are all G/N permutation modules over (mathbb {Z}_p, mathbb {Z}_p) and (mathbb {Z}_p) respectively. The necessity of the first two conditions is easily shown but the necessity of the third was not known. We apply a correspondence due to Butler, which associates to a (mathbb {Z}_p) (varvec{G})-lattice for an abelian (varvec{p})-group a set of simple combinatorial data, to demonstrate the necessity of the conditions, using the correspondence to construct highly non-trivial counterexamples to the claim that if both the (varvec{N})-invariants and the (varvec{N})-coinvariants of a given lattice (varvec{U}) are permutation modules, then so is (varvec{U}). Our approach, which is new, is to translate the desired properties to the combinatorial side, find the counterexample there, and translate it back to a lattice.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 4","pages":"1671 - 1680"},"PeriodicalIF":0.5,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742556","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

Almost Commuting Scheme of Symplectic Matrices and Quantum Hamiltonian Reduction 交映矩阵的几乎共通方案与量子哈密顿还原

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-07-17 DOI: 10.1007/s10468-024-10275-9

Pallav Goyal

{"title":"Almost Commuting Scheme of Symplectic Matrices and Quantum Hamiltonian Reduction","authors":"Pallav Goyal","doi":"10.1007/s10468-024-10275-9","DOIUrl":"10.1007/s10468-024-10275-9","url":null,"abstract":"<div>Losev introduced the scheme X of almost commuting elements (i.e., elements commuting upto a rank one element) of (mathfrak {g}=mathfrak {sp}(V)) for a symplectic vector space V and discussed its algebro-geometric properties. We construct a Lagrangian subscheme (X^{nil}) of X and show that it is a complete intersection of dimension (text {dim}(mathfrak {g})+frac{1}{2}text {dim}(V)) and compute its irreducible onents. We also study the quantum Hamiltonian reduction of the algebra (mathcal {D}(mathfrak {g})) of differential operators on the Lie algebra (mathfrak {g}) tensored with the Weyl algebra with respect to the action of the symplectic group, and show that it is isomorphic to the spherical subalgebra of a certain rational Cherednik algebra of Type C. We contruct a category (mathcal {C}_c) of (mathcal {D})-modules whose characteristic variety is contained in (X^{nil}) and construct an exact functor from this category to the category (mathcal {O}) of the above rational Cherednik algebra. Simple objects of the category (mathcal {C}_c) are mirabolic analogs of Lusztig’s character sheaves.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 4","pages":"1645 - 1669"},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10275-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718902","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

Localization of Triangulated Categories with Respect to Extension-Closed Subcategories 关于外延封闭子范畴的三角范畴本地化

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-05-31 DOI: 10.1007/s10468-024-10272-y

Yasuaki Ogawa

{"title":"Localization of Triangulated Categories with Respect to Extension-Closed Subcategories","authors":"Yasuaki Ogawa","doi":"10.1007/s10468-024-10272-y","DOIUrl":"10.1007/s10468-024-10272-y","url":null,"abstract":"<div>The aim of this paper is to develop a framework for localization theory of triangulated categories (mathcal {C}), that is, from a given extension-closed subcategory (mathcal {N}) of (mathcal {C}), we construct a natural extriangulated structure on (mathcal {C}) together with an exact functor (Q:mathcal {C}rightarrow widetilde{mathcal {C}}_mathcal {N}) satisfying a suitable universality, which unifies several phenomena. Precisely, a given subcategory (mathcal {N}) is thick if and only if the localization (widetilde{mathcal {C}}_mathcal {N}) corresponds to a triangulated category. In this case, Q is nothing other than the usual Verdier quotient. Furthermore, it is revealed that (widetilde{mathcal {C}}_mathcal {N}) is an exact category if and only if (mathcal {N}) satisfies a generating condition (textsf{Cone}(mathcal {N},mathcal {N})=mathcal {C}). Such an (abelian) exact localization (widetilde{mathcal {C}}_mathcal {N}) provides a good understanding of some cohomological functors (mathcal {C}rightarrow textsf{Ab}), e.g., the heart of t-structures on (mathcal {C}) and the abelian quotient of (mathcal {C}) by a cluster-tilting subcategory (mathcal {N}).</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1603 - 1640"},"PeriodicalIF":0.5,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197677","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

Birational Maps to Grassmannians, Representations and Poset Polytopes 通向格拉斯曼、表征和 Poset 多面体的双向映射

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2024-05-30 DOI: 10.1007/s10468-024-10273-x

Evgeny Feigin

引用次数: 0

On a Generalized Auslander-Reiten Conjecture 关于广义奥斯兰德-雷滕猜想

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-05-17 DOI: 10.1007/s10468-024-10271-z

Souvik Dey, Shinya Kumashiro, Parangama Sarkar

{"title":"On a Generalized Auslander-Reiten Conjecture","authors":"Souvik Dey, Shinya Kumashiro, Parangama Sarkar","doi":"10.1007/s10468-024-10271-z","DOIUrl":"10.1007/s10468-024-10271-z","url":null,"abstract":"<div>It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten condition (ARC). In this paper we explore (SAC) along with the several canonical change of rings (R rightarrow S). First, we prove the equivalence of (SAC) for R and R/xR, where x is a non-zerodivisor on R, and the equivalence of (SAC) and (SACC) for rings with positive depth, where (SACC) is the symmetric Auslander condition for modules with constant rank. The latter assertion affirmatively answers a question posed by Celikbas and Takahashi. Secondly, for a ring homomorphism (R rightarrow S), we prove that if S satisfies (SAC) (resp. (ARC)), then R also satisfies (SAC) (resp. (ARC)) if the flat dimension of S over R is finite. We also prove that (SAC) holds for R implies that (SAC) holds for S when R is Gorenstein and (S=R/Q^ell ), where Q is generated by a regular sequence of R and the length of the sequence is at least (ell ). This is a consequence of more general results about Ulrich ideals proved in this paper. Applying these results to determinantal rings and numerical semigroup rings, we provide new classes of rings satisfying (SAC). A relation between (SAC) and an invariant related to the finitistic extension degree is also explored.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1581 - 1602"},"PeriodicalIF":0.5,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061936","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

Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra 扩展海森堡-维拉索罗顶点算子代数的扭曲表示

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-30 DOI: 10.1007/s10468-024-10270-0

Hongyan Guo, Huaimin Li

{"title":"Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra","authors":"Hongyan Guo, Huaimin Li","doi":"10.1007/s10468-024-10270-0","DOIUrl":"10.1007/s10468-024-10270-0","url":null,"abstract":"<div>In this paper, we study simple weak and ordinary twisted modules of the extended Heisenberg-Virasoro vertex operator algebra (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). We first determine the full automorphism groups of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)) for all (ell _{1}, ell _{2},ell _{3},Fin {mathbb C}). They are isomorphic to certain subgroups of the general linear group (text {GL}_{2}({mathbb C})). Then for a family of finite order automorphisms (sigma _{r_{1},r_{2}}) of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)), we show that weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are in one-to-one correspondence with restricted modules of certain Lie algebras of level (ell _{123}), where (r_{1}, r_2in {mathbb N}). By this identification and vertex algebra theory, we give complete lists of simple ordinary (sigma _{r_{1},r_{2}})-twisted modules over (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). The results depend on whether F or (ell _{2}) is zero or not. Furthermore, simple weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are also investigated. For this, we introduce and study restricted modules (including Whittaker modules) of a new Lie algebra (mathcal {L}_{r_{1},r_{2}}) which is related to the mirror Heisenberg-Virasoro algebra.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1563 - 1580"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833522","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

The Mukai Conjecture for Fano Quiver Moduli 法诺震颤模的向猜想

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-26 DOI: 10.1007/s10468-024-10268-8

Markus Reineke

引用次数: 0

Galleries for Root Subsystems 根子系统图库

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-24 DOI: 10.1007/s10468-024-10269-7

Vladimir Shchigolev

引用次数: 0