3-Preprojective Algebras of Type D

Abstract: Given an algebra with finite global dimension, it is natural to consider two autoequivalences of its bounded derived category: the Serre functor and the shift functor. If a power of one is isomorphic to a power of the other, we say the algebra is fractional Calabi-Yau. Closely related are d-representation-finite algebras. These are algebras whose module category contains a d-cluster tilting subcategory, which is “manageable” even if the algebra has wild representation type. We will explain these concepts, and how they are connected, before presenting an infinite family of algebras which are both fractional Calabi-Yau and 2-representation-finite.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.