Twisted split category algebras as quasi-hereditary algebras

TL;DR

This paper proves that twisted split category algebras over a field of characteristic zero are quasi-hereditary, extending the understanding of their algebraic structure and representation theory.

Contribution

It establishes that twisted category algebras derived from split categories are quasi-hereditary, providing new insights into their algebraic properties.

Findings

Twisted split category algebras are quasi-hereditary.

The result holds over fields of characteristic zero.

The paper characterizes the algebraic structure of these algebras.

Abstract

A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field of characteristic 0 and let $\alpha$ be a 2-cocycle of $C$ with values in the unit group of $k$. Then the twisted category algebra $k_\alpha C$ is a quasi-hereditary algebra.