Pub Date : 2023-06-01DOI: 10.1142/s1005386723000184
Nan Gao, Xuanyu Liu, Jing Ma
Higher differential objects are investigated and used for addressing three general problems. Torsionless differential modules over path algebras are characterized. The adjoint triples between triangulated categories, involving derived categories and singularity categories, are allowed to be constructed from those between the abelian categories [Formula: see text] and [Formula: see text]. The partial silting properties between an abelian category [Formula: see text] and [Formula: see text] are transferred, and if moreover,[Formula: see text] is Frobenius, the partial silting objects of the stable monomorphism categories of [Formula: see text] are constructed from those of [Formula: see text].
{"title":"Silting Objects over the Stable Monomorphism Category of Higher Differential Objects","authors":"Nan Gao, Xuanyu Liu, Jing Ma","doi":"10.1142/s1005386723000184","DOIUrl":"https://doi.org/10.1142/s1005386723000184","url":null,"abstract":"Higher differential objects are investigated and used for addressing three general problems. Torsionless differential modules over path algebras are characterized. The adjoint triples between triangulated categories, involving derived categories and singularity categories, are allowed to be constructed from those between the abelian categories [Formula: see text] and [Formula: see text]. The partial silting properties between an abelian category [Formula: see text] and [Formula: see text] are transferred, and if moreover,[Formula: see text] is Frobenius, the partial silting objects of the stable monomorphism categories of [Formula: see text] are constructed from those of [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88906863","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000202
Jia-feng Lü, Panpan Wang, Ling Liu
Let [Formula: see text] be a BiHom-Hopf algebra and [Formula: see text] be an [Formula: see text]-BiHom-bimodule algebra, where the maps [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are bijective. We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra. Next we give a Morita context between the BiHom-subalgebra [Formula: see text] and the BiHom-L-R smash product [Formula: see text].
{"title":"On BiHom-L-R Smash Products","authors":"Jia-feng Lü, Panpan Wang, Ling Liu","doi":"10.1142/s1005386723000202","DOIUrl":"https://doi.org/10.1142/s1005386723000202","url":null,"abstract":"Let [Formula: see text] be a BiHom-Hopf algebra and [Formula: see text] be an [Formula: see text]-BiHom-bimodule algebra, where the maps [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are bijective. We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra. Next we give a Morita context between the BiHom-subalgebra [Formula: see text] and the BiHom-L-R smash product [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74914257","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000287
Xu Yang, Xiaomin Zhu, Jing Chen
The distance matrix of a connected graph [Formula: see text], denoted by [Formula: see text], is the matrix whose rows and columns are indexed by the vertex set [Formula: see text] such that the [Formula: see text]-entry is [Formula: see text], where [Formula: see text], [Formula: see text]. The distance signature [Formula: see text] of [Formula: see text] is the inertia of [Formula: see text]. In this paper, we determine the distance signature of the extended (co-extended) incidence graph of an affine design. Furthermore, we state that an open Graffiti conjecture is true for the extended (co-extended) incidence graphs of affine designs by investigating the lower bound of the matching number.
连通图[公式:见文]的距离矩阵，用[公式:见文]表示，是一个矩阵，它的行和列由顶点集[公式:见文]索引，使得[公式:见文]条目为[公式:见文]，其中[公式:见文]，[公式:见文]。[Formula: see text]的距离签名[Formula: see text]是[Formula: see text]的惯性。本文确定了仿射设计的扩展(共扩展)关联图的距离特征。此外，我们通过研究匹配数的下界，证明了对仿射设计的扩展(共扩展)关联图的开放涂鸦猜想是成立的。
{"title":"Distance Signatures of Extended and Co-extended Incidence Graphs of Affine Designs","authors":"Xu Yang, Xiaomin Zhu, Jing Chen","doi":"10.1142/s1005386723000287","DOIUrl":"https://doi.org/10.1142/s1005386723000287","url":null,"abstract":"The distance matrix of a connected graph [Formula: see text], denoted by [Formula: see text], is the matrix whose rows and columns are indexed by the vertex set [Formula: see text] such that the [Formula: see text]-entry is [Formula: see text], where [Formula: see text], [Formula: see text]. The distance signature [Formula: see text] of [Formula: see text] is the inertia of [Formula: see text]. In this paper, we determine the distance signature of the extended (co-extended) incidence graph of an affine design. Furthermore, we state that an open Graffiti conjecture is true for the extended (co-extended) incidence graphs of affine designs by investigating the lower bound of the matching number.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85882039","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000172
B. Hou, Jinzhong Wu
Let [Formula: see text] over a field [Formula: see text]. We give a clear characterization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of [Formula: see text] for any [Formula: see text], and the Gerstenhaber algebraic structure on Hochschild cohomology of [Formula: see text] for [Formula: see text].
{"title":"BV Structure on Hochschild Cohomology of Quantum Exterior Algebra with Two Variables","authors":"B. Hou, Jinzhong Wu","doi":"10.1142/s1005386723000172","DOIUrl":"https://doi.org/10.1142/s1005386723000172","url":null,"abstract":"Let [Formula: see text] over a field [Formula: see text]. We give a clear characterization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of [Formula: see text] for any [Formula: see text], and the Gerstenhaber algebraic structure on Hochschild cohomology of [Formula: see text] for [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82494022","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}
Pub Date : 2023-06-01DOI: 10.1142/s100538672300024x
Thomas Michael Keller, Yong Yang
Let [Formula: see text] be a faithful [Formula: see text]-module for a finite group [Formula: see text] and let[Formula: see text] be a prime dividing [Formula: see text]. An orbit [Formula: see text] for the action of [Formula: see text] on[Formula: see text] is regular if [Formula: see text], and is [Formula: see text]-regular if [Formula: see text]. In this note, we study two questions, one by the authors and one by Isaacs, related to the [Formula: see text]-regular orbits and regular orbits of the linear group actions.
{"title":"Regular and p-Regular Orbits of Solvable Linear Groups, II","authors":"Thomas Michael Keller, Yong Yang","doi":"10.1142/s100538672300024x","DOIUrl":"https://doi.org/10.1142/s100538672300024x","url":null,"abstract":"Let [Formula: see text] be a faithful [Formula: see text]-module for a finite group [Formula: see text] and let[Formula: see text] be a prime dividing [Formula: see text]. An orbit [Formula: see text] for the action of [Formula: see text] on[Formula: see text] is regular if [Formula: see text], and is [Formula: see text]-regular if [Formula: see text]. In this note, we study two questions, one by the authors and one by Isaacs, related to the [Formula: see text]-regular orbits and regular orbits of the linear group actions.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135887746","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000299
Zhilin Zhang, Shenglin Zhou
In this paper we present two new families of 2-[Formula: see text] designs with a flag-transitive and point-primitive automorphism group of product action type. More surprisingly, one of them is still a family of 2-[Formula: see text] designs with a flag-transitive and point-imprimitive automorphism group.
{"title":"On 2-(v,k,λ) Designs with Flag-Transitive Automorphism Groups of Product Action Type","authors":"Zhilin Zhang, Shenglin Zhou","doi":"10.1142/s1005386723000299","DOIUrl":"https://doi.org/10.1142/s1005386723000299","url":null,"abstract":"In this paper we present two new families of 2-[Formula: see text] designs with a flag-transitive and point-primitive automorphism group of product action type. More surprisingly, one of them is still a family of 2-[Formula: see text] designs with a flag-transitive and point-imprimitive automorphism group.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73046754","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000238
Dandan Zhang, H. Qu, Yanfeng Luo
A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.
{"title":"Finite p-Groups G with H′=G′ for Each A2-Subgroup H","authors":"Dandan Zhang, H. Qu, Yanfeng Luo","doi":"10.1142/s1005386723000238","DOIUrl":"https://doi.org/10.1142/s1005386723000238","url":null,"abstract":"A finite [Formula: see text]-group [Formula: see text] is called an [Formula: see text]-group if [Formula: see text]is the minimal non-negative integer such that all subgroups of index [Formula: see text] of [Formula: see text] are abelian. The finite [Formula: see text]-groups [Formula: see text] with [Formula: see text] for all [Formula: see text]-subgroups [Formula: see text] of [Formula: see text]are classified completely in this paper. As an application, a problem proposed by Berkovich is solved.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85100479","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000196
Payman Mahmood Hamaali, A. Mafi, H. Saremi
Let [Formula: see text] be the polynomial ring in [Formula: see text] variables over a field [Formula: see text] and [Formula: see text] be a matroidal ideal of [Formula: see text]. We show that [Formula: see text] is sequentially Cohen–Macaulay if and only if the [Formula: see text] has linear quotients. As a consequence, [Formula: see text] is sequentially Cohen–Macaulay if and only if [Formula: see text] is shellable.
设[公式:见文]为[公式:见文]域中变量[公式:见文]中的多项式环，[公式:见文]为[公式:见文]的矩阵理想。我们证明，当且仅当[公式:见文本]具有线性商时，[公式:见文本]是顺序Cohen-Macaulay。因此，当且仅当[Formula: see text]是可shell时，[Formula: see text]是顺序Cohen-Macaulay。
{"title":"A Characterization of Sequentially Cohen–Macaulay Matroidal Ideals","authors":"Payman Mahmood Hamaali, A. Mafi, H. Saremi","doi":"10.1142/s1005386723000196","DOIUrl":"https://doi.org/10.1142/s1005386723000196","url":null,"abstract":"Let [Formula: see text] be the polynomial ring in [Formula: see text] variables over a field [Formula: see text] and [Formula: see text] be a matroidal ideal of [Formula: see text]. We show that [Formula: see text] is sequentially Cohen–Macaulay if and only if the [Formula: see text] has linear quotients. As a consequence, [Formula: see text] is sequentially Cohen–Macaulay if and only if [Formula: see text] is shellable.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81867671","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}
Pub Date : 2023-06-01DOI: 10.1142/s1005386723000275
Imran Ahmed, Shahid Muhmood
We introduce first the spanning simplicial complex (SSC) of a multigraph [Formula: see text], which gives a generalization of the SSC associated with a simple graph [Formula: see text]. Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs [Formula: see text] with [Formula: see text] edges including [Formula: see text] multiple edges within and outside the cycle of length [Formula: see text], which are then used to compute the [Formula: see text]-vector and Hilbert series of face ring [Formula: see text] for the SSC[Formula: see text]. Moreover, we find the associated primes of the facet ideal [Formula: see text]. Finally, we device a formula for homology groups of [Formula: see text] and prove that the SSC of a family of uni-cyclic multigraphs is Cohen-Macaulay.
{"title":"Algebraic Characterization of SSC of Uni-Cyclic Multigraphs","authors":"Imran Ahmed, Shahid Muhmood","doi":"10.1142/s1005386723000275","DOIUrl":"https://doi.org/10.1142/s1005386723000275","url":null,"abstract":"We introduce first the spanning simplicial complex (SSC) of a multigraph [Formula: see text], which gives a generalization of the SSC associated with a simple graph [Formula: see text]. Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs [Formula: see text] with [Formula: see text] edges including [Formula: see text] multiple edges within and outside the cycle of length [Formula: see text], which are then used to compute the [Formula: see text]-vector and Hilbert series of face ring [Formula: see text] for the SSC[Formula: see text]. Moreover, we find the associated primes of the facet ideal [Formula: see text]. Finally, we device a formula for homology groups of [Formula: see text] and prove that the SSC of a family of uni-cyclic multigraphs is Cohen-Macaulay.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135887744","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}
Pub Date : 2023-04-17DOI: 10.1142/s1005386723000214
Sania Asif, Lipeng Luo, Y. Hong, Zhixiang Wu
Let [Formula: see text] be a finite Lie conformal algebra. We investigate the conformal derivation algebra [Formula: see text], conformal triple derivation algebra [Formula: see text] and generalized conformal triple derivation algebra [Formula: see text], focusing mainly on the connections among these derivation algebras. We also give a complete classification of (generalized) conformal triple derivation algebras on all finite simple Lie conformal algebras. In particular, [Formula: see text], where [Formula: see text] is a finite simple Lie conformal algebra. But for [Formula: see text], we obtain a conclusion that is closely related to [Formula: see text]. Finally, we introduce the definition of a triple homomorphism of Lie conformal algebras. Triple homomorphisms of all finite simple Lie conformal algebras are also characterized.
{"title":"Conformal Triple Derivations and Triple Homomorphisms of Lie Conformal Algebras","authors":"Sania Asif, Lipeng Luo, Y. Hong, Zhixiang Wu","doi":"10.1142/s1005386723000214","DOIUrl":"https://doi.org/10.1142/s1005386723000214","url":null,"abstract":"Let [Formula: see text] be a finite Lie conformal algebra. We investigate the conformal derivation algebra [Formula: see text], conformal triple derivation algebra [Formula: see text] and generalized conformal triple derivation algebra [Formula: see text], focusing mainly on the connections among these derivation algebras. We also give a complete classification of (generalized) conformal triple derivation algebras on all finite simple Lie conformal algebras. In particular, [Formula: see text], where [Formula: see text] is a finite simple Lie conformal algebra. But for [Formula: see text], we obtain a conclusion that is closely related to [Formula: see text]. Finally, we introduce the definition of a triple homomorphism of Lie conformal algebras. Triple homomorphisms of all finite simple Lie conformal algebras are also characterized.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79146894","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}
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