Homological systems and bocses

2020/12/26 by Ramos, Raymundo Bautista, Terrazas, Jesús Efrén Pérez, Castro, Leonardo Salmerón
#16E30 #16E45 #16G10 #16G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2012.13781

Abstract

We show that, up to Morita equivalence, any finite-dimensional algebra with a suitable homological system, admits an exact Borel subalgebra. 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.

Related

• Generalizations of the relationship between quasi-hereditary algebras and directed bocses
• Uniqueness of exact Borel subalgebras and bocses
• Quasi-hereditary algebras, exact Borel subalgebras, A-infinity-categories and boxes
• Uniqueness up to Inner Automorphism of Regular Exact Borel Subalgebras
• Exact Borel subalgebras of tensor algebras of quasi-hereditary algebras