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

Abstract

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--Hölder property (DJHP) fails for $\Lambda (A,B)$. This provides finite dimensional algebras of finite global dimension which do not satisfy DJHP.

19 pages. Algebra and Representation Theory, published online

References in corpus (2)

• Jordan-Hölder theorems for derived categories of derived discrete algebras
• Jordan Hölder theorems for derived module categories of piecewise hereditary algebras