$\tau$exceptional sequences
Abstract
We introduce the notions of $\tau$exceptional and signed $\tau$exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between the set of signed $\tau$exceptional sequences of length $t$, and (basic) ordered support $\tau$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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 DOI:
 10.48550/arXiv.1802.01169
 arXiv:
 arXiv:1802.01169
 Bibcode:
 2018arXiv180201169B
 Keywords:

 Mathematics  Representation Theory;
 16G20
 EPrint:
 28 pages. To appear in the Journal of Algebra