8 July 2026 — Padova

Quiver Heisenberg algebras and higher preprojective algebras

Martin Herschend, University of Uppsala

Abstract

In my talk I will discuss the quiver Heisenberg algebra associated to an acyclic quiver Q. It is a certain kind of central extension of the preprojective algebra of Q. Just as the preprojective algebra, the quiver Heisenberg algebra encodes important information about the path algebra of Q. In particular, it has very particular homological properties depending on if Q is of Dynkin type or not. I will discuss these in relation higher dimensional Auslander-Reiten theory by realizing a certain double cover of the quiver Heisenberg algebra as a higher preprojective algebra.

This talk is based on ongoing joint work with Hiroyuki Minamoto.