Mutations and the derived Picard group of the Brauer star algebra

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