# From quasi-hereditary algebras with exact Borel subalgebras to directed bocses

## TL;DR

This paper explores the relationship between quasi-hereditary algebras and directed bocses, providing a characterization of exact Borel subalgebras derived from them, enhancing understanding of their structural connections.

## Contribution

It offers a new characterization of exact Borel subalgebras associated with quasi-hereditary algebras via directed bocses, clarifying their structural relationship.

## Key findings

- Every quasi-hereditary algebra is Morita equivalent to the dual of a directed bocs.
- An explicit construction of exact Borel subalgebras from directed bocses is provided.
- The paper characterizes which exact Borel subalgebras arise from this construction.

## Abstract

Up to Morita equivalence, every quasi-hereditary algebra is the dual algebra of a directed bocs or coring. From the bocs, an exact Borel subalgebra is obtained. In this paper a characterisation of exact Borel subalgebras arising in this way is given.