Stability conditions on Brauer tree algebras

Abstract

We study the space of stability conditions attached to the derived category of $A_n$-mod for $A_n$ the Brauer tree algebra of the line with $n$ edges. These algebras arise in the study of cyclic defect blocks of group algebras, and they are also related to the zig-zag algebras introduced by Huerfano and Khovanov. We show that for the Brauer tree algebra $A_3$, the connected component of the natural heart of the space of stability conditions is simply connected. However, unlike certains examples arising in geometry, the Bridgeland homomorphism is not a covering map.

31 pages

References in corpus (1)

• Mutating Brauer trees