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Restricted Injective Dimensions over Cohen-Macaulay Rings 科恩-麦考莱环上的限制注入维数
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-03-19 DOI: 10.1007/s10468-024-10262-0
Michal Hrbek, Giovanna Le Gros
{"title":"Restricted Injective Dimensions over Cohen-Macaulay Rings","authors":"Michal Hrbek,&nbsp;Giovanna Le Gros","doi":"10.1007/s10468-024-10262-0","DOIUrl":"10.1007/s10468-024-10262-0","url":null,"abstract":"<div><p>We show that the small and large restricted injective dimensions coincide for Cohen-Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of Sather-Wagstaff and Totushek, we suggest a new definition of Cohen-Macaulay Hom injective dimension. We show that the class of Cohen-Macaulay Hom injective modules is the right constituent of a perfect cotorsion pair. Our approach relies on tilting theory, and in particular, on the explicit construction of the tilting module inducing the minimal tilting class recently obtained in (Hrbek et al. 2022).</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1373 - 1393"},"PeriodicalIF":0.5,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168499","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
Commutativity Preservers of Incidence Algebras 发生代数的交换性保全器
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-03-19 DOI: 10.1007/s10468-024-10265-x
Érica Z. Fornaroli, Mykola Khrypchenko, Ednei A. Santulo Jr
{"title":"Commutativity Preservers of Incidence Algebras","authors":"Érica Z. Fornaroli,&nbsp;Mykola Khrypchenko,&nbsp;Ednei A. Santulo Jr","doi":"10.1007/s10468-024-10265-x","DOIUrl":"10.1007/s10468-024-10265-x","url":null,"abstract":"<div><p>Let <i>I</i>(<i>X</i>, <i>K</i>) be the incidence algebra of a finite connected poset <i>X</i> over a field <i>K</i> and <i>D</i>(<i>X</i>, <i>K</i>) its subalgebra consisting of diagonal elements. We describe the bijective linear maps <span>(varphi :I(X,K)rightarrow I(X,K))</span> that strongly preserve the commutativity and satisfy <span>(varphi (D(X,K))=D(X,K))</span>. We prove that such a map <span>(varphi )</span> is a composition of a commutativity preserver of shift type and a commutativity preserver associated to a quadruple <span>((theta ,sigma ,c,kappa ))</span> of simpler maps <span>(theta )</span>, <span>(sigma )</span>, <i>c</i> and a sequence <span>(kappa )</span> of elements of <i>K</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1457 - 1476"},"PeriodicalIF":0.5,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168498","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
Criterion for Quasi-Heredity 准危险性标准
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-03-12 DOI: 10.1007/s10468-024-10263-z
Yuichiro Goto
{"title":"Criterion for Quasi-Heredity","authors":"Yuichiro Goto","doi":"10.1007/s10468-024-10263-z","DOIUrl":"10.1007/s10468-024-10263-z","url":null,"abstract":"<div><p>Dlab and Ringel showed that algebras being quasi-hereditary in all orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary. As a matter of fact, we consider permutations of indices, and if the algebra with permuted indices is quasi-hereditary, then we say that this permutation gives quasi-heredity. In this article, we give a criterion for adjacent transpositions giving quasi-heredity, in terms of homological conditions of standard or costandard modules over a given quasi-hereditary algebra.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1395 - 1403"},"PeriodicalIF":0.5,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105213","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
Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras 罗塔-巴克斯特列双桥、经典杨-巴克斯特方程和特殊 L-树枝状双桥
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-28 DOI: 10.1007/s10468-024-10261-1
Chengming Bai, Li Guo, Guilai Liu, Tianshui Ma
{"title":"Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras","authors":"Chengming Bai,&nbsp;Li Guo,&nbsp;Guilai Liu,&nbsp;Tianshui Ma","doi":"10.1007/s10468-024-10261-1","DOIUrl":"10.1007/s10468-024-10261-1","url":null,"abstract":"<div><p>This paper extends the well-known fact that a Rota-Baxter operator of weight 0 on a Lie algebra induces a pre-Lie algebra, to the level of bialgebras. We first show that a nondegenerate symmetric bilinear form that is invariant on a Rota-Baxter Lie algebra of weight 0 gives such a form that is left-invariant on the induced pre-Lie algebra and thereby gives a special L-dendriform algebra. This fact is obtained as a special case of Rota-Baxter Lie algebras with an adjoint-admissible condition, for a representation of the Lie algebra to admit a representation of the Rota-Baxter Lie algebra on the dual space. This condition can also be naturally formulated for Manin triples of Rota-Baxter Lie algebras, which can in turn be characterized in terms of bialgebras, thereby extending the Manin triple approach to Lie bialgebras. In the case of weight 0, the resulting Rota-Baxter Lie bialgebras give rise to special L-dendriform bialgebras, lifting the aforementioned connection that a Rota-Baxter Lie algebra induces a pre-Lie algebra to the level of bialgebras. The relationship between these two classes of bialgebras is also studied in terms of the coboundary cases, classical Yang-Baxter equations and <span>(mathcal {O})</span>-operators.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1347 - 1372"},"PeriodicalIF":0.5,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004540","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
Two (mathbb {Z})-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra 与维拉索罗共形代数有关的两个 $mathbb {Z}$ -Graded 无限列共形代数
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-24 DOI: 10.1007/s10468-024-10260-2
Xiaoqing Yue, Shun Zou
{"title":"Two (mathbb {Z})-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra","authors":"Xiaoqing Yue,&nbsp;Shun Zou","doi":"10.1007/s10468-024-10260-2","DOIUrl":"10.1007/s10468-024-10260-2","url":null,"abstract":"<div><p>In this paper, we study two <span>(mathbb {Z})</span>-graded infinite Lie conformal algebras, which are closely related to a class of Lie algebras of the generalized Block type, and which both have a quotient algebra isomorphic to the Virasoro conformal algebra. We concretely determine their isomorphic mappings, conformal derivations, extensions by a one-dimensional center under some conditions, finite conformal modules and <span>(mathbb {Z})</span>-graded free intermediate series modules.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1311 - 1345"},"PeriodicalIF":0.5,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956253","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
Soergel Calculus with Patches 带补丁的索格尔微积分
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-23 DOI: 10.1007/s10468-024-10259-9
Leonardo Maltoni
{"title":"Soergel Calculus with Patches","authors":"Leonardo Maltoni","doi":"10.1007/s10468-024-10259-9","DOIUrl":"10.1007/s10468-024-10259-9","url":null,"abstract":"<div><p>We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We use this description to recover basic results about these complexes, namely the categorification of the relations of the braid group and the Rouquier formula.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1287 - 1309"},"PeriodicalIF":0.5,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956178","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
Recollements of Derived Categories from Two-Term Big Tilting Complexes 从两期大倾斜复合体衍生类别的重元素
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-19 DOI: 10.1007/s10468-024-10258-w
Huabo Xu
{"title":"Recollements of Derived Categories from Two-Term Big Tilting Complexes","authors":"Huabo Xu","doi":"10.1007/s10468-024-10258-w","DOIUrl":"10.1007/s10468-024-10258-w","url":null,"abstract":"<div><p>We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting complexes over rings. Given a two-term big tilting complex over an arbitrary associative ring, we show that the derived module category of its (derived) endomorphism ring is a recollement of the one of the given ring and the one of a universal localization of the endomorphism ring. This recollement generalizes the one established for a good tilting module of projective dimension at most one.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1267 - 1285"},"PeriodicalIF":0.5,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920798","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
Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations 椭圆量子环状代数、Z-代数结构与表示
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-13 DOI: 10.1007/s10468-024-10251-3
Hitoshi Konno, Kazuyuki Oshima
{"title":"Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations","authors":"Hitoshi Konno,&nbsp;Kazuyuki Oshima","doi":"10.1007/s10468-024-10251-3","DOIUrl":"10.1007/s10468-024-10251-3","url":null,"abstract":"<div><p>We introduce a new elliptic quantum toroidal algebra <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span> associated with an arbitrary toroidal algebra <span>({mathfrak {g}}_{tor})</span>. We show that <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span> contains two elliptic quantum algebras associated with a corresponding affine Lie algebra <span>(widehat{mathfrak {g}})</span> as subalgebras. They are analogue of the horizontal and the vertical subalgebras in the quantum toroidal algebra <span>(U_{q,kappa }({mathfrak {g}}_{tor}))</span>. A Hopf algebroid structure is introduced as a co-algebra structure of <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span> using the Drinfeld comultiplication. We also investigate the <i>Z</i>-algebra structure of <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span> and show that the <i>Z</i>-algebra governs the irreducibility of the level <span>((k (ne 0),l))</span>-infinite dimensional <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span>-modules in the same way as in the elliptic quantum group <span>(U_{q,p}(widehat{mathfrak {g}}))</span>. As an example, we construct the level (1, <i>l</i>) irreducible representation of <span>(U_{q,kappa ,p}({mathfrak {g}}_{tor}))</span> for the simply laced <span>({mathfrak {g}}_{tor})</span>. We also construct the level (0, 1) representation of <span>(U_{q,kappa ,p}({mathfrak {gl}}_{N,tor}))</span> and discuss a conjecture on its geometric interpretation as an action on the torus equivariant elliptic cohomology of the affine <span>(A_{N-1})</span> quiver variety.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1137 - 1175"},"PeriodicalIF":0.5,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772620","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
Presentations of Braid Groups of Type A Arising from ((m+2))-angulations of Regular Polygons 由正多边形的 $$(m+2)$$ -angulation 产生的 A 型辫状花序群的演示文稿
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-02 DOI: 10.1007/s10468-024-10257-x
Davide Morigi
{"title":"Presentations of Braid Groups of Type A Arising from ((m+2))-angulations of Regular Polygons","authors":"Davide Morigi","doi":"10.1007/s10468-024-10257-x","DOIUrl":"10.1007/s10468-024-10257-x","url":null,"abstract":"<div><p>Coloured quiver mutation, introduced by Buan, A.B., Thomas, H (Adv. Math. <b>222</b>(3), 971–995 2009), gives a combinatorial interpretation of tilting in higher cluster categories. In type <i>A</i> work of Baur, K., Marsh, B. (Trans. Am. Math. Soc. <b>360</b>(11), 5789-5803 2008) shows that <i>m</i>-coloured quivers and <i>m</i>-coloured quiver mutations have a nice geometrical description, given in terms of <span>((m+2))</span>-angulations of a regular polygon, and rotations of an <i>m</i>-diagonal. In this paper, using such correspondence, we describe presentations of braid groups of type <i>A</i> arising from coloured quivers of mutation type <i>A</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1237 - 1265"},"PeriodicalIF":0.5,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10257-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139663400","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
Unique Factorization for Tensor Products of Parabolic Verma Modules 抛物线维尔马模块张量乘的唯一因式分解
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-02-01 DOI: 10.1007/s10468-024-10254-0
K. N. Raghavan, V. Sathish Kumar, R. Venkatesh, Sankaran Viswanath
{"title":"Unique Factorization for Tensor Products of Parabolic Verma Modules","authors":"K. N. Raghavan,&nbsp;V. Sathish Kumar,&nbsp;R. Venkatesh,&nbsp;Sankaran Viswanath","doi":"10.1007/s10468-024-10254-0","DOIUrl":"10.1007/s10468-024-10254-0","url":null,"abstract":"<div><p>Let <span>(mathfrak g)</span> be a symmetrizable Kac-Moody Lie algebra with Cartan subalgebra <span>(mathfrak h)</span>. We prove a unique factorization property for tensor products of parabolic Verma modules. More generally, we prove unique factorization for products of characters of parabolic Verma modules when restricted to certain subalgebras of <span>(mathfrak h)</span>. These include fixed point subalgebras of <span>(mathfrak h)</span> under subgroups of diagram automorphisms of <span>(mathfrak g)</span> and twisted graph automorphisms in the affine case.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1203 - 1220"},"PeriodicalIF":0.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139663407","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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