Examples of finite dimensional algebras which do not satisfy the derived Jordan--Hölder property

Qunhua Liu, Dong Yang

Published 2017-04-03Version 1

We construct a matrix algebra $\Lambda(A,B)$ from two given finite dimensional elementary algebras $A$ and $B$ and give some sufficient conditions on $A$ and $B$ under which the derived Jordan--H\"older property (DJHP) fails for $\Lambda(A,B)$. This provides finite dimensional algebras of finite global dimension which do not satisfy DJHP.