On the derived Picard group of the Brauer star algebra

Abstract

In this paper we show that the derived Picard group $TrPic(A)$ of the Brauer star algebra of type $(n,t)$ is generated by shift, $Pic(A)$ and equivalences $\{H_i\}_{i=1}^n$ in the case $t>1$, where $H_i$ were shown to satisfy the relations of the braid group on the affine diagram $\widetilde{A}_{n-1}$ by Schaps and Zakay-Illouz. In the multiplicity free case we show that $TrPic(A)$ is generated by a slightly bigger set.