arXiv subjects
Publications and source records attributed to Håvard Utne Terland.
We characterise those basic and connected Nakayama algebras $Λ$ for which the mutation of $τ$-exceptional sequences respects the braid group relations. We show that this is the case if and only if $Λ$ is hereditary or all indecomposable projective $Λ$-modules have length at least $|Λ|$.
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.