Exceptional versus $\tau$-exceptional sequences for the Auslander algebra of $K[x]/(x^t)$

Abstract

For $\mathcal{A}_t$, the Auslander algebra of $K[x]/(x^t)$, it is shown that every complete exceptional sequence of $\mathcal{A}_t$-modules is a complete $\tau$-exceptional sequence. Moreover, it is established that the mutation of complete $\tau$-exceptional sequences generalises the mutation of complete exceptional sequences in the category of $\mathcal{A}_t$-modules.