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

DOI: 10.2140/pjm.2019.302.599

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

Milestones

Received: 23 September 2017

Revised: 1 October 2018

Accepted: 4 December 2018

Published: 27 November 2019