Algebra Seminar: Homological properties of quiver Heisenberg algebras

The seminar will be held via Zoom link (meeting ID: 645 5572 6999, please contact the organizer for passcode)

Abstract: In my talk I will introduce 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. More specifically, it gives rise to a universal almost split sequence. This in turn leads to very particular homological properties depending on if Q is of Dynkin type or not.

I will discuss these in relation to the derived Auslander-Iyama correspondence of Jasso-Muro and to Iyama's higher dimensional Auslander-Reiten theory.

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

This is a seminar in our algebra seminar series.