arXiv:1709.03618 Abstract | arXiv Analytics

arXiv:1709.03618 [math.RT]Abstract References Reviews Resources

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

Published 2017-09-11Version 1

We classify spherical modules and full exceptional sequences of modules over the Auslander algebra of $k[x]/(x^t)$. 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.

Comments: 20 pages, 2 full page figures, many small figures

Categories: math.RT, math.AG

Subjects: 16D90, 16G20, 16S38, 18E30

Keywords: auslander algebra, spherical modules, right symmetric group actions, right mutations, spherical twists

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