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Algebras and Representation Theory最新文献

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Framization and deframization 框架化和反框架化
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-06-18 DOI: 10.1007/s10468-025-10341-w
Francesca Aicardi, Jesús Juyumaya, Paolo Papi
{"title":"Framization and deframization","authors":"Francesca Aicardi,&nbsp;Jesús Juyumaya,&nbsp;Paolo Papi","doi":"10.1007/s10468-025-10341-w","DOIUrl":"10.1007/s10468-025-10341-w","url":null,"abstract":"<div><p>Starting from the geometric construction of the framed braid group, we define and study the framization of several Brauer-type monoids and also the set partition monoid, all of which appear in knot theory. We introduce the concept of deframization, which is a procedure to obtain a tied monoid from a given framed monoid. Furthermore, we show in detail how this procedure works on the monoids mentioned above. We also discuss the framization and deframization of some algebras, which are deformations, respectively, of the framized and deframized monoids discussed here.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 6","pages":"1469 - 1506"},"PeriodicalIF":0.6,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027154","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
Toric Vector Bundles, Valuations and Tropical Geometry 环向矢量束，估值和热带几何
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-05-15 DOI: 10.1007/s10468-025-10336-7
Kiumars Kaveh, Christopher Manon
{"title":"Toric Vector Bundles, Valuations and Tropical Geometry","authors":"Kiumars Kaveh,&nbsp;Christopher Manon","doi":"10.1007/s10468-025-10336-7","DOIUrl":"10.1007/s10468-025-10336-7","url":null,"abstract":"<div><p>A toric vector bundle <span>(mathcal {E})</span> is a torus equivariant vector bundle on a toric variety. We give a valuation theoretic and tropical point of view on toric vector bundles. We present three (equivalent) classifications of toric vector bundles, which should be regarded as repackagings of the Klyachko data of compatible <span>(mathbb {Z})</span>-filtrations of a toric vector bundle: (1) as piecewise linear maps to space of <span>(mathbb {Z})</span>-valued valuations, (2) as valuations with values in the semifield of piecewise linear functions, and (3) as points in tropical linear ideals over the semifield of piecewise linear functions. Moreover, we interpret the known criteria for ampleness and global generation of <span>(mathcal {E})</span> as convexity conditions on its piecewise linear map in (1). Finally, using (2) we associate to <span>(mathcal {E})</span> a collection of polytopes indexed by elements of a certain (representable) matroid encoding the dimensions of weight spaces of global sections of <span>(mathcal {E})</span>. This recovers and extends the Di Rocco-Jabbusch-Smith matriod and parliament of polytopes of <span>(mathcal {E})</span>. This is a follow up paper to Kaveh and Manon. Math. Zeitschrift <b>302</b>(3), 1367-1392 \u0000(2022).</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 6","pages":"1439 - 1467"},"PeriodicalIF":0.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027094","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
The Defining Characteristic Case of the Representations of (textrm{GL}_{n}) and (textrm{SL}_{n}) Over Principal Ideal Local Rings 主理想局部环上(textrm{GL}_{n})和(textrm{SL}_{n})表示的定义特征情形
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2025-04-21 DOI: 10.1007/s10468-025-10333-w
Nariel Monteiro
{"title":"The Defining Characteristic Case of the Representations of (textrm{GL}_{n}) and (textrm{SL}_{n}) Over Principal Ideal Local Rings","authors":"Nariel Monteiro","doi":"10.1007/s10468-025-10333-w","DOIUrl":"10.1007/s10468-025-10333-w","url":null,"abstract":"<div><p>Let <span>(W_{r}(mathbb {F}_{q}))</span> be the ring of Witt vectors of length <i>r</i> with residue field <span>(mathbb {F}_{q})</span> of characteristic <i>p</i>. In this paper, we study the defining characteristic case of the representations of <span>(textrm{GL}_{n})</span> and <span>(textrm{SL}_{n})</span> over the principal ideal local rings <span>(W_{r}(mathbb {F}_{q}))</span> and <span>(mathbb {F}_{q}[t]/t^{r})</span>. Let <span>({textbf{G}})</span> be either <span>(textrm{GL}_{n})</span> or <span>(textrm{SL}_{n})</span> and <i>F</i> a perfect field of characteristic <i>p</i>, we prove that for most <i>p</i> the group algebras <span>(F[{textbf{G}}(W_{r}(mathbb {F}_{q}))])</span> and <span>(F[{textbf{G}}(mathbb {F}_{q}[t]/t^{r})])</span> are not stably equivalent of Morita type. Thus, the group algebras <span>(F[{textbf{G}}(W_{r}(mathbb {F}_{q}))])</span> and <span>(F[{textbf{G}}(mathbb {F}_{q}[t]/t^{r})])</span> are not isomorphic in the defining characteristic case.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 2","pages":"669 - 677"},"PeriodicalIF":0.5,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100146","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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