Generalizations of the relationship between quasi-hereditary algebras and directed bocses

TL;DR

This paper extends the known correspondence between quasi-hereditary algebras and directed bocses to broader classes of filtered algebras, enriching the theoretical framework of algebra representations.

Contribution

It generalizes the relationship to include $ ext{Δ}$-filtered and $ar{ ext{Δ}}$-filtered algebras, broadening the scope of the original correspondence.

Findings

Extended the correspondence to $ ext{Δ}$-filtered algebras.

Extended the correspondence to $ar{ ext{Δ}}$-filtered algebras.

Provided a unified framework for these algebra classes.

Abstract

Koenig, K\"ulshammer and Ovsienko showed that Morita equivalence classes of quasi-hereditary algebras are in one-to-one correspondence with equivalence classes of the module categories over directed bocses. In this article, we extend this result to $\Delta$-filtered algebras and $\overline{\Delta}$-filtered algebras.