Mutating signed -exceptional sequences

Abstract

AbstractWe establish some properties of $\tau$ -exceptional sequences for finite-dimensional algebras. In an earlier paper, we established a bijection between the set of ordered support $\tau$ -tilting modules and the set of complete signed $\tau$ -exceptional sequences. We describe the action of the symmetric group on the latter induced by its natural action on the former. Similarly, we describe the effect on a $\tau$ -exceptional sequence obtained by mutating the corresponding ordered support $\tau$ -tilting module via a construction of Adachi-Iyama-Reiten.