τ-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 t ≤ n, there is a bijection between the set of signed τ-exceptional sequences of length, and (basic) ordered support τ-rigid objects within decomposable 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.

Metadata

Authors/Creators:

Buan, AB
Marsh, B https://orcid.org/0000-0002-4268-8937

© 2021 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords:

2-term silting object; Bongartz complement; cluster morphism category; exceptional sequence; Finite-dimensional algebra; perpendicular category; τ-exceptional sequence; τ-rigid module; τ-tilting theory

Dates: