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arXiv · 1401.6952

On the derived Picard group of the Brauer star algebra

Alexandra Zvonareva
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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.

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Alexandra Zvonareva. 2015-07-28. On the derived Picard group of the Brauer star algebra. https://arxiv.org/abs/1401.6952

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