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On fibered Burnside rings, fiber change maps and cyclic fiber groups 在纤维伯恩赛德环上，有纤维变化图和循环纤维群
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-25 DOI: 10.1016/j.jpaa.2025.107961
Benjamín García, Alberto G. Raggi-Cárdenas
{"title":"On fibered Burnside rings, fiber change maps and cyclic fiber groups","authors":"Benjamín García,&nbsp;Alberto G. Raggi-Cárdenas","doi":"10.1016/j.jpaa.2025.107961","DOIUrl":"10.1016/j.jpaa.2025.107961","url":null,"abstract":"<div><div>Fibered Burnside rings appear as Grothendieck rings of fibered permutation representations of a finite group, generalizing Burnside rings and monomial representation rings. Their species, primitive idempotents and their conductors are of particular interest in representation theory as they encode information related to the structure of the group. In this note, we introduce fiber change maps between fibered Burnside rings, and we present results on their functoriality and naturality with respect to biset operations. We present some advances on the conductors for cyclic fiber groups, and fully determine them in particular cases, covering a wide range of interesting examples.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107961"},"PeriodicalIF":0.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Model structure from one hereditary complete cotorsion pair 一个遗传完全扭转对的模型结构
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-25 DOI: 10.1016/j.jpaa.2025.107958
Jian Cui, Xue-Song Lu, Pu Zhang
{"title":"Model structure from one hereditary complete cotorsion pair","authors":"Jian Cui,&nbsp;Xue-Song Lu,&nbsp;Pu Zhang","doi":"10.1016/j.jpaa.2025.107958","DOIUrl":"10.1016/j.jpaa.2025.107958","url":null,"abstract":"<div><div>In contrast with the Hovey correspondence of abelian model structures from two complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from one hereditary complete cotorsion pair. The aim of this paper is to extend this result to weakly idempotent complete exact categories, by adding the condition of heredity of the complete cotorsion pair. In fact, even for abelian categories, this condition of heredity should be added. This construction really gives model structures which are not necessarily exact in the sense of Gillespie. The correspondence of Beligiannis and Reiten of weakly projective model structures also holds for weakly idempotent complete exact categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107958"},"PeriodicalIF":0.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Module monoidal categories as categorification of associative algebras 结合代数的模一元范畴
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-24 DOI: 10.1016/j.jpaa.2025.107959
Sebastian Heinrich
{"title":"Module monoidal categories as categorification of associative algebras","authors":"Sebastian Heinrich","doi":"10.1016/j.jpaa.2025.107959","DOIUrl":"10.1016/j.jpaa.2025.107959","url":null,"abstract":"<div><div>In <span><span>[12]</span></span>, the notion of a module tensor category was introduced as a braided monoidal central functor <span><math><mi>F</mi><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>T</mi></math></span> from a braided monoidal category <span><math><mi>V</mi></math></span> to a monoidal category <span><math><mi>T</mi></math></span>, which is a monoidal functor <span><math><mi>F</mi><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>T</mi></math></span> together with a braided monoidal lift <span><math><msup><mrow><mi>F</mi></mrow><mrow><mi>Z</mi></mrow></msup><mo>:</mo><mi>V</mi><mo>⟶</mo><mi>Z</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> to the Drinfeld center of <span><math><mi>T</mi></math></span>. This is a categorification of a unital associative algebra <em>A</em> over a commutative ring <em>R</em> via a ring homomorphism <span><math><mi>f</mi><mo>:</mo><mi>R</mi><mo>⟶</mo><mi>Z</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> into the center of <em>A</em>. In this paper, we want to categorify the characterization of an associative algebra as a (not necessarily unital) ring <em>A</em> together with an <em>R</em>–module structure over a commutative ring <em>R</em>, such that multiplication in <em>A</em> and action of <em>R</em> on <em>A</em> are compatible. In doing so, we introduce the more general notion of <em>non–unital module monoidal categories</em> and obtain 2–categories of non–unital and unital module monoidal categories, their functors and natural transformations. We will show that in the unital case the latter definition is equivalent to the definition in <span><span>[12]</span></span> by explicitly writing down an equivalence of 2–categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107959"},"PeriodicalIF":0.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Injective generation for graded rings 梯度环的内射生成
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-24 DOI: 10.1016/j.jpaa.2025.107960
Panagiotis Kostas, Chrysostomos Psaroudakis
{"title":"Injective generation for graded rings","authors":"Panagiotis Kostas,&nbsp;Chrysostomos Psaroudakis","doi":"10.1016/j.jpaa.2025.107960","DOIUrl":"10.1016/j.jpaa.2025.107960","url":null,"abstract":"<div><div>In this paper we investigate injective generation for graded rings. We first examine the relation between injective generation and graded injective generation for graded rings. We then reduce the study of injective generation for graded rings to the study of injective generation for certain Morita context rings and we provide sufficient conditions for injective generation of the latter. We then provide necessary and sufficient conditions so that injectives generate for tensor rings and for trivial extension rings. We provide two proofs for the class of tensor rings, one uses covering theory and the other uses the framework of cleft extensions of module categories. We finally prove injective generation for twisted tensor products of finite dimensional algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107960"},"PeriodicalIF":0.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Affine pavings of quiver flag varieties 箭旗品种仿射饰面
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-21 DOI: 10.1016/j.jpaa.2025.107953
Xiaoxiang Zhou
{"title":"Affine pavings of quiver flag varieties","authors":"Xiaoxiang Zhou","doi":"10.1016/j.jpaa.2025.107953","DOIUrl":"10.1016/j.jpaa.2025.107953","url":null,"abstract":"<div><div>In this article, we construct affine pavings for quiver partial flag varieties when the quiver is of Dynkin type. To achieve our results, we extend methods from Cerulli-Irelli–Esposito–Franzen–Reineke and Maksimau as well as techniques from Auslander–Reiten theory.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107953"},"PeriodicalIF":0.7,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 pro-nilpotent Lawrence-Krammer-Bigelow representation 亲零Lawrence-Krammer-Bigelow表示
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107952
Martin Palmer , Arthur Soulié
{"title":"The pro-nilpotent Lawrence-Krammer-Bigelow representation","authors":"Martin Palmer ,&nbsp;Arthur Soulié","doi":"10.1016/j.jpaa.2025.107952","DOIUrl":"10.1016/j.jpaa.2025.107952","url":null,"abstract":"<div><div>We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having the original LKB representation as its bottom layer. We also construct analogous pro-nilpotent towers of representations of surface braid groups and loop braid groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107952"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 isomorphism problem for rational group algebras of finite metacyclic groups 有限亚环群的有理群代数的同构问题
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107951
Àngel García-Blázquez, Ángel del Río
{"title":"The isomorphism problem for rational group algebras of finite metacyclic groups","authors":"Àngel García-Blázquez,&nbsp;Ángel del Río","doi":"10.1016/j.jpaa.2025.107951","DOIUrl":"10.1016/j.jpaa.2025.107951","url":null,"abstract":"<div><div>We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where the line separating positive and negative solutions to the Isomorphism Problem for group algebras lies.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107951"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Deformations of unitary Howe dual pairs 幺正Howe对偶的变形
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107948
Dan Ciubotaru , Hendrik De Bie , Marcelo De Martino , Roy Oste
{"title":"Deformations of unitary Howe dual pairs","authors":"Dan Ciubotaru ,&nbsp;Hendrik De Bie ,&nbsp;Marcelo De Martino ,&nbsp;Roy Oste","doi":"10.1016/j.jpaa.2025.107948","DOIUrl":"10.1016/j.jpaa.2025.107948","url":null,"abstract":"<div><div>We study deformations of the Howe pairs <span><math><mo>(</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> to the context of a rational Cherednik algebra <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> associated with a real reflection group <em>G</em> acting on a real vector space <em>E</em> of even dimension. For each pair, we show that the Lie (super)algebra structure of one partner is preserved under the deformation, which leads to a joint decomposition of the standard module or its tensor product with a spinor space. For the case where <em>E</em> is two-dimensional and <em>G</em> is a dihedral group, we provide complete descriptions for the deformed pair and the relevant joint-decomposition.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107948"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Generalized (co)homology of symmetric quandles over homogeneous Beck modules 齐次Beck模上对称堆的广义（co）同调
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107956
Biswadeep Karmakar, Deepanshi Saraf, Mahender Singh
{"title":"Generalized (co)homology of symmetric quandles over homogeneous Beck modules","authors":"Biswadeep Karmakar,&nbsp;Deepanshi Saraf,&nbsp;Mahender Singh","doi":"10.1016/j.jpaa.2025.107956","DOIUrl":"10.1016/j.jpaa.2025.107956","url":null,"abstract":"<div><div>A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily oriented. In this paper, we introduce the category of symmetric quandle modules and prove that these modules completely determine the Beck modules in the category of symmetric quandles. Consequently, this establishes suitable coefficient objects for constructing appropriate (co)homology theories. We develop an extension theory of modules over symmetric quandles, and propose a generalized (co)homology theory for symmetric quandles with coefficients in a homogeneous Beck module, which also recovers the symmetric quandle (co)homology developed by Kamada and Oshiro (2010) <span><span>[16]</span></span>. Our constructions also apply to symmetric racks. We conclude by establishing an explicit isomorphism between the second cohomology of a symmetric quandle and the first cohomology of its associated group.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107956"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line 具有最大皮卡数的一般类型曲面的无限多新序列收敛于塞韦里线
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107957
Nguyen Bin , Vicente Lorenzo
{"title":"Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line","authors":"Nguyen Bin ,&nbsp;Vicente Lorenzo","doi":"10.1016/j.jpaa.2025.107957","DOIUrl":"10.1016/j.jpaa.2025.107957","url":null,"abstract":"<div><div>Examples of algebraic surfaces of general type with maximal Picard number are not abundant in the literature. Moreover, most known examples either possess low invariants, lie near the Noether line <span><math><msup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>2</mn><mi>χ</mi><mo>−</mo><mn>6</mn></math></span> or are somewhat scattered. A notable exception is Persson's sequence of double covers of the projective plane with maximal Picard number, whose invariants converge to the Severi line <span><math><msup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>4</mn><mi>χ</mi></math></span>. This note is devoted to the construction of infinitely many new sequences of surfaces of general type with maximal Picard number whose invariants converge to the Severi line.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107957"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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