We introduce the notion of a (signed) 𝜏-exceptional sequence for a finite-dimensional algebra, which can be regarded as the generalization of a classical exceptional sequence considered in the hereditary case. The new sequences behave well for both non-hereditary and hereditary algebras. The work is motivated by the signed exceptional sequences introduced, in the hereditary case, by Igusa-Torodov, and by 𝜏-tilting theory. We show that there is a bijection between the set of complete signed exceptional sequences and ordered basic support 𝜏-tilting objects.
Joint work with Aslak Bakke Buan (NTNU).
This seminar forms part of the Isaac Newton Institute programme Cluster algebras and representation theory.
