Ozone Groups and Centers of Skew Polynomial Rings.

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. [ABSTRACT FROM AUTHOR]

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