Calabi-Yau Nichols algebras of Hecke type

TL;DR

This paper investigates Nichols algebras of Hecke type, establishing conditions under which they possess a rigid dualizing complex and characterizing when they are Calabi-Yau algebras.

Contribution

It provides a characterization of Calabi-Yau Nichols algebras of Hecke type based on Noetherianity and finite global dimension.

Findings

Existence of a rigid dualizing complex under certain conditions

Necessary and sufficient conditions for Calabi-Yau property

Abstract

Let $R$ be a Nichols algebra of Hecke type. In this paper, we show that if $R$ is Noetherian and of finite global dimension, then $R$ has a rigid dualizing complex. We then give a necessary and sufficient condition for $R$ to be a Calabi-Yau algebra.