Homological systems and bocses

We show that, up to Morita equivalence, any standardly stratified algebra, admits an exact Borel subalgebra. In fact, we show this in the more general case of finite-dimensional algebras possessing an admissible homological system. This generalizes a theorem by Koenig, Külshammer, and Ovsienko, whic...

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Bibliographic Details
Published inJournal of algebra Vol. 617; pp. 192 - 274
Main Authors Bautista, R., Pérez, E., Salmerón, L.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2023
Subjects
Bocs
Differential tensor algebra
Ditalgebra
Exact Borel subalgebras
Homological systems
Standardly filtered modules
16E30
Differential tensor algebra
Bocs
Ditalgebra
16G20
16E45
16G10
Homological systems
Standardly filtered modules
Exact Borel subalgebras
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Summary:We show that, up to Morita equivalence, any standardly stratified algebra, admits an exact Borel subalgebra. In fact, we show this in the more general case of finite-dimensional algebras possessing an admissible homological system. This generalizes a theorem by Koenig, Külshammer, and Ovsienko, which holds for quasi-hereditary algebras. Our proof follows the same general scheme proposed by these authors, in a more general context: we associate a differential graded tensor algebra with relations, using the structure of A∞-algebra of a suitable Yoneda algebra, and use its category of modules to describe the category of filtered modules associated to the given homological system.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.11.006