  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.
