Mutation of $\tau$-exceptional sequences for acyclic quivers over local algebras

Abstract

Let $k$ be an algebraically closed field. Let $R$ be a local commutative finite dimensional $k$-algebra and let $Q$ be a quiver with no loops or oriented cycles. We show that mutation of $\tau$-exceptional sequences over $\Lambda =R{\otimes }_{k}kQ\cong RQ$ in the sense of Buan, Hanson, and Marsh coincides with the classical mutation of exceptional sequences defined by Crawley-Boevey and Ringel. In particular, the braid group acts transitively on the set of complete $\tau$-exceptional sequences in $\text{mod }\Lambda$.

19 pages. V2: Added Section 4 "RQ-lattices". Minor changes. arXiv admin note: text overlap with arXiv:2402.10301 by other authors