Applying recent results by Lowen-Van den Bergh we show that Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra. More precisely, the corresponding Hochschild complexes are linked by a quasi-isomorphism of B-infinity-algebras.
应用Lowen-Van den Bergh的最新结果，我们证明了Hochschild上同调作为Gerstenhaber代数在Koszul-Moore对偶下是保持的。更准确地说，对应的Hochschild复合体是由b无穷代数的拟同构连接起来的。
{"title":"A remark on Hochschild cohomology and Koszul\u0000 duality","authors":"B. Keller","doi":"10.1090/CONM/761/15312","DOIUrl":"https://doi.org/10.1090/CONM/761/15312","url":null,"abstract":"Applying recent results by Lowen-Van den Bergh we show that Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra. More precisely, the corresponding Hochschild complexes are linked by a quasi-isomorphism of B-infinity-algebras.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115619612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This short note is devoted to motivate and clarify the notion of sequential walk introduced by the authors in a previous work. We also give some applications of this concept.
这篇短文致力于激发和澄清作者在以前的工作中引入的顺序行走的概念。我们还给出了这一概念的一些应用。
{"title":"A note on sequential walks","authors":"I. Assem, M. J. Redondo, R. Schiffler","doi":"10.1090/CONM/761/15307","DOIUrl":"https://doi.org/10.1090/CONM/761/15307","url":null,"abstract":"This short note is devoted to motivate and clarify the notion of sequential walk introduced by the authors in a previous work. We also give some applications of this concept.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117002727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a purely ring-theoretic characterization of fuchsian singularities. (4) Expoloit their singularity categories and their Grothendieck groups.
{"title":"The algebraic theory of fuchsian\u0000 singularties","authors":"H. Lenzing","doi":"10.1090/CONM/761/15315","DOIUrl":"https://doi.org/10.1090/CONM/761/15315","url":null,"abstract":"This article has the following aims: \u0000(1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. \u0000(2) Discuss their relationship to mathematical objects of a different nature. \u0000(3) Provide a purely ring-theoretic characterization of fuchsian singularities. \u0000(4) Expoloit their singularity categories and their Grothendieck groups.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129961003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this survey we present the criterion for tameness of strongly simply connected algebras due to Brustle, de la Pena and Skowronski. We recall relevant concepts of representation theory and discuss some applications and connections to other problems.
本文给出了Brustle、de la Pena和Skowronski所给出的强单连通代数的驯服性判据。我们回顾了表征理论的相关概念，并讨论了一些应用和与其他问题的联系。
{"title":"On tame strongly simply connected\u0000 algebras","authors":"S. Kasjan, Andrzej Skowro'nski","doi":"10.1090/CONM/761/15311","DOIUrl":"https://doi.org/10.1090/CONM/761/15311","url":null,"abstract":"In this survey we present the criterion for tameness of strongly simply connected algebras due to Brustle, de la Pena and Skowronski. We recall relevant concepts of representation theory and discuss some applications and connections to other problems.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"421 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115248142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson tableaux and show that they characterize the isomorphism types of finite direct sums of such cyclic embeddings.
{"title":"Finite direct sums of cyclic\u0000 embeddings","authors":"J. Kosakowska, M. Schmidmeier","doi":"10.1090/CONM/761/15314","DOIUrl":"https://doi.org/10.1090/CONM/761/15314","url":null,"abstract":"In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson tableaux and show that they characterize the isomorphism types of finite direct sums of such cyclic embeddings.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125072817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.
{"title":"Cycle-finite modules over artin\u0000 algebras","authors":"P. Malicki, Andrzej Skowro'nski","doi":"10.1090/CONM/761/15316","DOIUrl":"https://doi.org/10.1090/CONM/761/15316","url":null,"abstract":"We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms from the infinite Jacobson radical of the module category.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130074127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We survey recent development of the study of finite-dimensional selfinjective algebras over a field which are socle equivalent to selfinjective orbit algebras of tilted type.
本文综述了场上有限维自射代数的研究进展，这些代数与倾斜型自射轨道代数是完全等价的。
{"title":"Socle deformations of selfinjective orbit\u0000 algebras of tilted type","authors":"Andrzej Skowro'nski, K. Yamagata","doi":"10.1090/CONM/761/15319","DOIUrl":"https://doi.org/10.1090/CONM/761/15319","url":null,"abstract":"We survey recent development of the study of finite-dimensional selfinjective algebras over a field which are socle equivalent to selfinjective orbit algebras of tilted type.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128352683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this result to the study of algebras with finitely many orbits with respect to the action of (the double product) of the group of units.
{"title":"A characterization of representation infinite\u0000 quiver settings","authors":"Grzegorz Bobiński","doi":"10.1090/CONM/761/15308","DOIUrl":"https://doi.org/10.1090/CONM/761/15308","url":null,"abstract":"We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this result to the study of algebras with finitely many orbits with respect to the action of (the double product) of the group of units.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"27 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113994018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $KDelta$ be the incidence algebra associated with a finite poset $Delta$ over the algebraically closed field $K$. We present a study of incidence algebras $KDelta$ that are piecewise hereditary, which we denominate PHI algebras. We explore the simply connectedness of PHI algebras, and we give a positive answer to the so-called Skowro'nski problem for $KDelta$ a PHI algebra of type $mathcal{H}$, with connected quiver of tilting objects $mathcal{K}_{D^b (mathcal{H})}$: the group $HH^1(KDelta)$ is trivial if, and only if, $KDelta$ is a simply connected algebra. We determine an upper bound for the strong global dimension of PHI algebra; furthermore, we extend this result to sincere algebras proving that the strong global dimension of a sincere piecewise hereditary algebra is less or equal to three. If $A$ is a representation-infinite quasi-tilted algebra of quiver-sheaf type with a sincere indecomposable module $M$ (thus a special type of PHI algebra), then $M$ is exceptional, which makes it possible to construct a PHI algebra of wild type as the form of one-point extension algebra $KDelta[M]$ of some PHI algebra $KDelta$ by the canonical sincere $KDelta$-module $M$.
{"title":"Piecewise hereditary incidence\u0000 algebras","authors":"E. Marcos, Marcelo Moreira","doi":"10.1090/CONM/761/15317","DOIUrl":"https://doi.org/10.1090/CONM/761/15317","url":null,"abstract":"Let $KDelta$ be the incidence algebra associated with a finite poset $Delta$ over the algebraically closed field $K$. We present a study of incidence algebras $KDelta$ that are piecewise hereditary, which we denominate PHI algebras. \u0000We explore the simply connectedness of PHI algebras, and we give a positive answer to the so-called Skowro'nski problem for $KDelta$ a PHI algebra of type $mathcal{H}$, with connected quiver of tilting objects $mathcal{K}_{D^b (mathcal{H})}$: the group $HH^1(KDelta)$ is trivial if, and only if, $KDelta$ is a simply connected algebra. We determine an upper bound for the strong global dimension of PHI algebra; furthermore, we extend this result to sincere algebras proving that the strong global dimension of a sincere piecewise hereditary algebra is less or equal to three. If $A$ is a representation-infinite quasi-tilted algebra of quiver-sheaf type with a sincere indecomposable module $M$ (thus a special type of PHI algebra), then $M$ is exceptional, which makes it possible to construct a PHI algebra of wild type as the form of one-point extension algebra $KDelta[M]$ of some PHI algebra $KDelta$ by the canonical sincere $KDelta$-module $M$.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130547185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thick subcategories of the stable category of\u0000 modules over the exterior algebra","authors":"O. Kerner, D. Zacharia","doi":"10.1090/CONM/761/15313","DOIUrl":"https://doi.org/10.1090/CONM/761/15313","url":null,"abstract":"We study thick subcategories defined by modules of complexity one in $underline{md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114713075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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