The Ozone groups of PI Artin-Schelter regular algebras are abelian

TL;DR

This paper proves that the ozone group of any PI Artin-Schelter regular algebra is abelian and shows that for Calabi-Yau cases, the homological determinant of this group action is trivial, answering a key open question.

Contribution

It establishes the abelian nature of ozone groups in PI Artin-Schelter regular algebras and characterizes their homological determinants in Calabi-Yau cases.

Findings

Ozone group of PI Artin-Schelter regular algebra is abelian

Homological determinant is trivial for Calabi-Yau PI Artin-Schelter regular algebra

Answers a question posed by Chan-Gaddis-Won-Zhang

Abstract

We prove that the ozone group of any PI Artin-Schelter regular algebra is abelian, which answers a question of Chan-Gaddis-Won-Zhang. For any Calabi-Yau PI Artin-Schelter regular algebra, we prove that the homological determinant of its ozone group acting on it is trivial.