May 22, 2025, 14:00 +0200
Padova, Torre Archimede 1BC45

A transitive braid group action

Håvard Terland, NTNU

Abstract

Exceptional sequences over hereditary algebras enjoy nice combinatorial properties and interesting facts are still discovered, for example by Igusa and Sen who have recently investigated a connection to rooted trees. Of particular interest to us, there is a well-known transitive braid group action on exceptional sequences over hereditary algebras (Crawley-Boevey 93). For \(\tau\)-exceptional sequences, a proposed generalization of exceptional sequences introduced by Buan and Marsh, a mutation generalizing the mutation of exceptional sequences was recently proposed by Buan, Marsh and Hanson. This mutation is neither transitive nor respects the braid group relations in general. We show that for a class of cyclic Nakayama algebras, however, the mutation does induce a transitive braid group action.