On quasi-hereditary algebras

TL;DR

This paper introduces a new criterion for identifying quasi-hereditary algebras by reducing the problem to associated monomial algebras, providing explicit conditions for monomial cases.

Contribution

It offers a novel reduction method and explicit criteria for determining quasi-heredity in finite dimensional algebras, simplifying the verification process.

Findings

Reduction of the quasi-hereditary problem to monomial algebras

Explicit necessary and sufficient criterion for monomial algebras

Simplified verification process for quasi-hereditary property

Abstract

Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that the question can be reduced to showing that a closely associated monomial algebra is quasi-hereditary. For monomial algebras, we give an explicit, easily verifiable, necessary and sufficient criterion to determine whether it is quasi-hereditary.