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

Abstract

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.

19 pages, 2 full page figures, many small figures; v2: additional reference, results unchanged, fixed a formula and improved structure

References in corpus (3)

• A reduction theorem for $\tau$-rigid modules
• Lattice structure of Weyl groups via representation theory of preprojective algebras
• Tilting chains of negative curves on rational surfaces

Cited by in corpus (2)

• Witt groups of abelian categories and perverse sheaves
• Rigid divisors on surfaces