Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

Abstract

We investigate conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra, and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that $\mathrm {hdet}(\mu _A) = 1$ for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra $A$.