Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

TL;DR

This paper explores conditions under which Ext-algebras in triangulated categories become Frobenius algebras, proving a conjecture relating to the Nakayama automorphism in skew Calabi-Yau algebras.

Contribution

It establishes criteria for Ext-algebras to be Frobenius and confirms a conjecture about the Nakayama automorphism in noetherian Artin-Schelter regular algebras.

Findings

Ext-algebras can be Frobenius under certain conditions

Proves hdet(μ_A) = 1 for skew Calabi-Yau algebras

Provides explicit computation of Nakayama automorphism

Abstract

We investigate the 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 hdet($\mu_A$) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.