2021/09/23 by Håvard Utne Terland, Terland, Håvard Utne
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2109.11464
openalex publication_date 2021/09/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Important objects of study in τ-tilting theory include the τ-tilting pairs over an algebra on the form kQ/I, with kQ being a path algebra and I an admissible ideal. In this paper, we study aspects of the combinatorics of mutation quivers of support τ-tilting pairs, simply called mutation quivers. In particular, we are interested in identifying connected components of the underlying graphs of such quivers. We give a class of algebras with two simple modules such that every algebra in the class has at most two connected components in its mutation quiver, generalizing a result by Demonet, Iyama and Jasso (2017). We also give examples of algebras with strictly more than two components in their mutation quivers.