Reduction Techniques to Identify Connected Components of Mutation Quivers

arXiv2109.11464MaRDI QIDQ6378405

Håvard Utne Terland

Publication date: 23 September 2021

Abstract: Important objects of study in $au$-tilting theory include the $au$-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 $au$-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.

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