3-Preprojective Algebras of Type D

Abstract

We present a family of selfinjective algebras of type D, which arise from the 3-preprojective algebras of type A by taking a ${\mathbb{Z}}_3$-quotient. We show that a subset of these are themselves 3-preprojective algebras, and that the associated 2-representation-finite algebras are fractional Calabi-Yau. In addition, we show our work is connected to modular invariants for SU(3).

31 pages, v3 follows peer review

References in corpus (5)

• Selfinjective quivers with potential and 2-representation-finite algebras
• Simplicial structures in higher Auslander-Reiten theory
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• Skew group algebras of Jacobian algebras
• The Nakayama automorphism of a self-injective preprojective algebra