Work

Ozone Groups and Centers of Skew Polynomial Rings

Year: 2023

Type: article

Abstract: We introduce the ozone group of a noncommutative algebra $A$, defined as the group of automorphisms of $A$, which fix every element of its center. In order to initiate the study of ozone groups, we study polynomial identity (PI) skew polynomial rings, which have long proved to be a fertile testing ground in noncommutative algebra. Using the ozone group and other invariants defined herein, we give explicit conditions for the center of a PI skew polynomial ring to be Gorenstein (resp. regular) in low dimension.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnad235

Authors: Kenneth Chan, Jason Gaddis, Robert Won, James J Zhang

Institutions: University of Washington, Miami University, George Washington University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Topics in Noncommutative Algebra, Topics in noncommutative algebra 2022: homological regularities