τ-exceptional sequences
| Autor: | Aslak Bakke Buan, Bethany Marsh |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Rank (linear algebra) 010102 general mathematics 01 natural sciences Combinatorics Set (abstract data type) Integer 0103 physical sciences Bijection 010307 mathematical physics 0101 mathematics Algebra over a field Mathematics::Representation Theory Indecomposable module Mathematics |
| Zdroj: | Journal of Algebra. 585:36-68 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2021.04.038 |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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