Two derived equivalences for higher Auslander algebras of type AOberseminar Algebra und Darstellungstheorie

by Wei Xing (Uppsala University)

Thursday Sep 3, 2026, 4:15 PM → 5:15 PM Europe/Berlin

Endenicher Allee 60/1-008-Seminarraum (Mathezentrum)

Given a positive integer d, a d-Auslander algebra A is characterized by the property that gldim A <= d+1 <= domdim A. Iyama showed that such an algebra is always obtained as the endomorphism algebra of a d-cluster tilting object in a module category. Starting from a linear A_n quiver, Iyama constructed an infinite family of d-Auslander algebras A_n^{d+1} called higher Auslander algebras of type A.

In this talk, I will present a derived equivalence between A_n^d and the incidence algebra of the poset of lattice paths in a d by n rectangle. Building on this combinatorial model for A_n^d, we construct a second derived equivalence between A_n^d and an nd-representation finite algebra when n and d are coprime. As a consequence, we show that the lattice of rational Dyck paths is fractionally Calabi-Yau.