2018/02/04 by Aslak Bakke Buan, Buan, Aslak Bakke, Bethany Marsh +1
Computer Science · Mathematics · #16G20 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Approximation Theory and Sequence Spaces #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1802.01169
openalex publication_date 2018/02/04 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
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.