Abstract
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.
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