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Initial Ideal of a General Rational or Elliptic Curve on Quadrics 二次曲面上一般有理曲线或椭圆曲线的初始理想
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-06-06 DOI: 10.1007/s10468-026-10401-9
Francesca Cioffi, Davide Franco, Giovanna Ilardi
{"title":"Initial Ideal of a General Rational or Elliptic Curve on Quadrics","authors":"Francesca Cioffi,&nbsp;Davide Franco,&nbsp;Giovanna Ilardi","doi":"10.1007/s10468-026-10401-9","DOIUrl":"10.1007/s10468-026-10401-9","url":null,"abstract":"<div><p>Over an algebraically closed field of characteristic zero, we prove that the generic initial ideal with respect to the degree reverse lexicographic term order of a general rational or elliptic curve on quadrics is almost revlex. Following constructive arguments, our proof combines features of a pencil of quadrics, interpolation methods and the notion of double generic initial ideal.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10401-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148247755","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
The i-Quantum Group (textbf{U}^imath (n)), II: Presenting their (varvec{q})-Schur Algebras i-量子群(textbf{U}^imath (n))， II：表示它们的(varvec{q}) -Schur代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-04-14 DOI: 10.1007/s10468-026-10390-9
Jian Chen, Jie Du
{"title":"The i-Quantum Group (textbf{U}^imath (n)), II: Presenting their (varvec{q})-Schur Algebras","authors":"Jian Chen,&nbsp;Jie Du","doi":"10.1007/s10468-026-10390-9","DOIUrl":"10.1007/s10468-026-10390-9","url":null,"abstract":"<div><p>Since the establishment of the quantum Schur–Weyl duality in Jimbo (Lett. Math. Phys. <b>11</b>, 247–252, 1986), the duality pair <span>((textbf{U}(mathfrak {gl}_n),varvec{mathcal {H}}(mathfrak S_r)))</span> of type <i>A</i> has been extended to the duality pairs <span>((textbf{U}^jmath (n),varvec{mathcal {H}}(B_r)))</span> and <span>((textbf{U}^imath (n),varvec{mathcal {H}}(C_r)))</span> in the Hecke algebra series in Bao and Wang (Astérisque <b>402</b>, vii+134, 2018), where <span>(textbf{U}^jmath (n),textbf{U}^imath (n))</span> are <i>i</i>-quantum groups arising from certain quantum symmetric pairs. The quantum Schur algebra associated with the pair <span>((textbf{U}(mathfrak {gl}_n),varvec{mathcal {H}}(mathfrak S_r)))</span> has a nice and simple presentation; see Doty and Giaquinto \u0000(2002). In this paper, we tackle the presentation problem for the <i>i</i>-quantum Schur algebras associated with the duality pair <span>((textbf{U}^imath (n),varvec{mathcal {H}}(C_r)))</span>. Such a <i>q</i>-Schur algebra is called the hyperoctahedral <i>q</i>-Schur algebras in Green (J. Algebra <b>192</b>, 418–438, 1997). See Bhattacharya \u0000(2026) for the <span>(textbf{U}^jmath (n))</span> case. Building on the explicit epimorphism <span>(phi _{n,r}^imath )</span> from the <i>i</i>-quantum group <span>(textbf{U}^imath (n))</span> to the hyperoctahedral <i>q</i>-Schur algebras <span>(mathcal {S}^imath (n,r))</span> (see Du and Wu, Pacific J. Math. <b>320</b>(1), 61–101, 2022), we compute the kernel of <span>(phi _{n,r}^imath )</span> in terms of generators. This results in a presentation for <span>(mathcal {S}^imath (n,r))</span> with defining relations which include not only the Doty–Giaquinto’s diagonal relations but also some tridiagonal relations.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"653 - 696"},"PeriodicalIF":0.6,"publicationDate":"2026-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10390-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752456","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
On a Question of Auslander and Bridger on 2-Reflexive Modules 关于Auslander和Bridger关于2-自反模块的问题
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-30 DOI: 10.1007/s10468-026-10392-7
René Marczinzik
{"title":"On a Question of Auslander and Bridger on 2-Reflexive Modules","authors":"René Marczinzik","doi":"10.1007/s10468-026-10392-7","DOIUrl":"10.1007/s10468-026-10392-7","url":null,"abstract":"<div><p>We answer a question raised by Auslander and Bridger by showing that not every 2-reflexive module is reflexive.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"721 - 723"},"PeriodicalIF":0.6,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10392-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752450","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
(infty )-Dold-Kan Correspondence via Representation Theory (infty )-基于表征理论的dold - kan对应
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-26 DOI: 10.1007/s10468-026-10388-3
Chiara Sava
{"title":"(infty )-Dold-Kan Correspondence via Representation Theory","authors":"Chiara Sava","doi":"10.1007/s10468-026-10388-3","DOIUrl":"10.1007/s10468-026-10388-3","url":null,"abstract":"<div><p>We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory: indeed, our result is a derivator-theoretic version of the <span>(infty )</span>-Dold-Kan correspondence for bounded chain complexes. Moreover, our equivalence can also be realized as an action of a spectral bimodule in the setting of universal tilting theory developed by Groth and Šťovíček.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"565 - 607"},"PeriodicalIF":0.6,"publicationDate":"2026-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10388-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752451","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
The Higher-Order Hom-Associative Weyl Algebras 高阶共轭Weyl代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-25 DOI: 10.1007/s10468-026-10391-8
Per Bäck
{"title":"The Higher-Order Hom-Associative Weyl Algebras","authors":"Per Bäck","doi":"10.1007/s10468-026-10391-8","DOIUrl":"10.1007/s10468-026-10391-8","url":null,"abstract":"<div><p>We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as hom-associative algebras. We also show that these hom-associative Weyl algebras arise naturally as hom-associative iterated differential polynomial rings, that they contain no zero divisors, are power-associative only when associative, and that they are simple. We then determine their commuters, nuclei, centers, and derivations. Last, we classify all hom-associative Weyl algebras up to isomorphism and conjecture that all nonzero homomorphisms between any two isomorphic hom-associative Weyl algebras are isomorphisms. The latter conjecture turns out to be stably equivalent to the Dixmier Conjecture, and hence also to the Jacobian Conjecture.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"697 - 719"},"PeriodicalIF":0.6,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10391-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752457","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
Acyclic Toric Sheaves 无环环面轮轴
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-23 DOI: 10.1007/s10468-026-10383-8
Klaus Altmann, Andreas Hochenegger, Frederik Witt
{"title":"Acyclic Toric Sheaves","authors":"Klaus Altmann,&nbsp;Andreas Hochenegger,&nbsp;Frederik Witt","doi":"10.1007/s10468-026-10383-8","DOIUrl":"10.1007/s10468-026-10383-8","url":null,"abstract":"<div><p>Let <span>(mathcal {E})</span> be a torus-linearised reflexive sheaf over a smooth projective toric variety. Generalising a theorem of Perlman and Smith, we prove an explicit sufficient condition for <span>(mathcal {E})</span> to be acyclic via Weil decorations.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"411 - 422"},"PeriodicalIF":0.6,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10383-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752377","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
Non-factorizable Ribbon Hopf Algebras 不可因子带状Hopf代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-18 DOI: 10.1007/s10468-026-10382-9
Quentin Faes, Maksymilian Manko
{"title":"Non-factorizable Ribbon Hopf Algebras","authors":"Quentin Faes,&nbsp;Maksymilian Manko","doi":"10.1007/s10468-026-10382-9","DOIUrl":"10.1007/s10468-026-10382-9","url":null,"abstract":"<div><p>Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to provide invariants of 4-dimensional 2-handlebodies up to 2-deformations. We prove that some of the invariants derived from these examples are invariants dependent only on the boundary or on the presentation of the fundamental group of the 2-handlebody.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"353 - 409"},"PeriodicalIF":0.6,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752452","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 Quantum Cluster Algebra Structure on the Semi-Derived Hall Algebra 半派生霍尔代数上的量子簇代数结构
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-13 DOI: 10.1007/s10468-026-10389-2
Alessandro Contu
{"title":"A Quantum Cluster Algebra Structure on the Semi-Derived Hall Algebra","authors":"Alessandro Contu","doi":"10.1007/s10468-026-10389-2","DOIUrl":"10.1007/s10468-026-10389-2","url":null,"abstract":"<div><p>Using Hernandez–Leclerc’s isomorphism between the derived Hall algebra of a representation-finite quiver <i>Q</i> and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of <i>Q</i>, we lift the (quantum) cluster algebra structure of the quantum Grothendieck ring to the semi-derived Hall algebra, introduced by Gorsky, of the category of bounded complexes of projective modules over the path algebra of <i>Q</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"609 - 651"},"PeriodicalIF":0.6,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752449","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
Duality Properties for Induced and Coinduced Representations in Positive Characteristic 正特征中诱导表示和共诱导表示的对偶性质
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-11 DOI: 10.1007/s10468-026-10384-7
Sophie Chemla
{"title":"Duality Properties for Induced and Coinduced Representations in Positive Characteristic","authors":"Sophie Chemla","doi":"10.1007/s10468-026-10384-7","DOIUrl":"10.1007/s10468-026-10384-7","url":null,"abstract":"<div><p>Let <i>k</i> be a field of positive characteristic <span>(p&gt;2)</span>. Generalizing a result of Farnsteiner and Strade (Math. Z., <b>206</b>, 153–168, 1991), we study the links between coinduced representations and induced representations in the case of restricted Lie superalgebras. As a corollary, we prove a duality property concerning the kernel of coinduced representations of Lie <i>k</i>-superalgebras. This property was already proved by Duflo (Invent. Math., <b>67</b>, 385–393, 1982) for Lie algebras in any characteristic under more restrictive finiteness conditions. It was then generalized to Lie superalgebras in characteristic 0 in previous works Chemla (PhD, 1990; Annales de l’Institut Fourier, <b>44</b>, 1067–1090, 1994 and Mathematische Annalen, <b>297</b>, 371–382, 1994).</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"423 - 442"},"PeriodicalIF":0.6,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10384-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752448","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
1-Cycle Deformations for Yetter-Drinfeld Coalgebras 叶特-德林菲尔德代数的1环变形
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-03-11 DOI: 10.1007/s10468-026-10377-6
Daniel Bulacu, Blas Torrecillas
{"title":"1-Cycle Deformations for Yetter-Drinfeld Coalgebras","authors":"Daniel Bulacu,&nbsp;Blas Torrecillas","doi":"10.1007/s10468-026-10377-6","DOIUrl":"10.1007/s10468-026-10377-6","url":null,"abstract":"<div><p>For a quasi-Hopf algebra <i>H</i>, we study two types of 1-cycle deformations for a coalgebra <i>C</i> within the category of Yetter-Drinfeld modules over <i>H</i>, <span>({}_H^H{mathcal YD})</span>. The two deformations produce <i>C</i>-comodule structures in <span>({}_H^H{mathcal YD})</span> and new coalgebra structures on <i>C</i> in <span>({}_H^H{mathcal YD})</span>, respectively. We show that the isomorphism types of these structures are described by a 1-homology <span>({mathcal H}^1_H(C, H_0))</span> that we will introduce. Then we apply our results to the so called symplectic fermion quasi-Hopf algebras, algebras recently introduced by Farsad, Gainutdinov and Runkel.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 2","pages":"279 - 329"},"PeriodicalIF":0.6,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10377-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147752395","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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