Twisted split category algebras as quasi-hereditary algebras

Abstract

A category is called {\em split} if for every morphism $s:X\to Y$ there exists a morphism $t:Y\to X$ 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.

11 pages. Added Section 4 on construction of standard modules. Final version

References in corpus (1)

• Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero