We classify spherical modules and full exceptional sequences of modules over the Auslander
algebra of
.
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