Buan, AB and Marsh, B orcid.org/0000-0002-4268-8937 (2021) τ-exceptional sequences. Journal of Algebra. ISSN 0021-8693
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.
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Copyright, Publisher and Additional Information: | © 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. | ||||
Keywords: | Finite-dimensional algebra; exceptional sequence; τ-exceptional sequence; τ-rigid module; τ-tilting theory; 2-term silting object; perpendicular category; Bongartz complement; cluster morphism category | ||||
Dates: |
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 11 Jun 2021 11:50 | ||||
Last Modified: | 02 Jun 2022 00:38 | ||||
Status: | Published online | ||||
Publisher: | Elsevier | ||||
Identification Number: | https://doi.org/10.1016/j.jalgebra.2021.04.038 |
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