On the definition of multi-Koszul modules

In [8] we introduced the notion of multi-Koszul algebra: it is an extension of the definition of generalized Koszul algebra given by R. Berger in [1] for homogeneous algebras (see also [7]) that can be applied to any nonnegatively graded connected algebra over a field k. The goal of this article is...

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Autor principal: Herscovich, E.
Formato: JOUR
Materias:
A∞-algebras
Homological algebra
Koszul algebra
Yoneda algebra
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v499_n_p478_Herscovich
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00218693_v499_n_p478_Herscovich2023-10-03T14:21:36Z On the definition of multi-Koszul modules Herscovich, E. A∞-algebras Homological algebra Koszul algebra Yoneda algebra In [8] we introduced the notion of multi-Koszul algebra: it is an extension of the definition of generalized Koszul algebra given by R. Berger in [1] for homogeneous algebras (see also [7]) that can be applied to any nonnegatively graded connected algebra over a field k. The goal of this article is on the one hand to properly extend the notion of multi-Koszul algebra to the case where the base ring K is a product of copies of a field k, which a priori allows us to treat quiver algebras, and on the other hand to introduce the notion of multi-Koszul module such that it extends the usual definition of generalized Koszul module over a generalized Koszul algebra. We show eventually that multi-Koszul algebras and multi-Koszul modules are strongly linked via the notion of one-point extensions, as in the case of generalized Koszul algebras. Moreover, we describe the complete structure of right A∞-module on ExtA •(M,K) over ExtA •(K,K), where M is a multi-Koszul module over a multi-Koszul algebra A, extending a result in [9]. As a corollary, we obtain that the underlying right module structure of ExtA •(M,K) over ExtA •(K,K) is generated by the component of cohomological degree zero, as in the case of generalized Koszul modules over generalized Koszul algebras. © 2017 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v499_n_p478_Herscovich
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A∞-algebras
Homological algebra
Koszul algebra
Yoneda algebra
spellingShingle A∞-algebras
Homological algebra
Koszul algebra
Yoneda algebra
Herscovich, E.
On the definition of multi-Koszul modules
topic_facet A∞-algebras
Homological algebra
Koszul algebra
Yoneda algebra
description In [8] we introduced the notion of multi-Koszul algebra: it is an extension of the definition of generalized Koszul algebra given by R. Berger in [1] for homogeneous algebras (see also [7]) that can be applied to any nonnegatively graded connected algebra over a field k. The goal of this article is on the one hand to properly extend the notion of multi-Koszul algebra to the case where the base ring K is a product of copies of a field k, which a priori allows us to treat quiver algebras, and on the other hand to introduce the notion of multi-Koszul module such that it extends the usual definition of generalized Koszul module over a generalized Koszul algebra. We show eventually that multi-Koszul algebras and multi-Koszul modules are strongly linked via the notion of one-point extensions, as in the case of generalized Koszul algebras. Moreover, we describe the complete structure of right A∞-module on ExtA •(M,K) over ExtA •(K,K), where M is a multi-Koszul module over a multi-Koszul algebra A, extending a result in [9]. As a corollary, we obtain that the underlying right module structure of ExtA •(M,K) over ExtA •(K,K) is generated by the component of cohomological degree zero, as in the case of generalized Koszul modules over generalized Koszul algebras. © 2017 Elsevier Inc.
format JOUR
author Herscovich, E.
author_facet Herscovich, E.
author_sort Herscovich, E.
title On the definition of multi-Koszul modules
title_short On the definition of multi-Koszul modules
title_full On the definition of multi-Koszul modules
title_fullStr On the definition of multi-Koszul modules
title_full_unstemmed On the definition of multi-Koszul modules
title_sort on the definition of multi-koszul modules
url http://hdl.handle.net/20.500.12110/paper_00218693_v499_n_p478_Herscovich
work_keys_str_mv AT herscoviche onthedefinitionofmultikoszulmodules
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