Vol. 302, No. 2, 2019

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Exceptional sequences and spherical modules for the Auslander algebra of $\boldsymbol k[x]/(x^t)$

Lutz Hille and David Ploog

Vol. 302 (2019), No. 2, 599–625
Abstract

We classify spherical modules and full exceptional sequences of modules over the Auslander algebra of $k\left[x\right]∕\left({x}^{t}\right)$. We categorify the left and right symmetric group actions on these exceptional sequences to two braid group actions: of spherical twists along simple modules, and of right mutations. In particular, every such exceptional sequence is obtained by spherical twists from a standard sequence, and likewise for right mutations.

Keywords
Auslander algebra, full exceptional sequence, exceptional module, spherical module
Mathematical Subject Classification 2010
Primary: 16D90
Secondary: 16G20, 16S38, 18E30