Tau-exceptional sequences

Abstract

We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer , there is a bijection between the set of signed τ-exceptional sequences of length t, and (basic) ordered support τ-rigid objects with t indecomposable direct summands. If the algebra is hereditary, our notions coincide with exceptional and signed exceptional sequences. The latter were recently introduced by Igusa and Todorov, who constructed a similar bijection in the hereditary setting.