On the discriminant of twisted tensor products
Jason Gaddis, Ellen Kirkman, W. Frank Moore
TL;DR
This paper develops formulas for calculating the discriminant of noncommutative algebras formed via twisted tensor products, enabling the analysis of automorphism groups in these complex algebraic structures.
Contribution
It introduces general formulas for discriminants of twisted tensor products, extending previous methods to Ore and skew group extensions.
Findings
Formulas for discriminants of Ore extensions
Formulas for discriminants of skew group extensions
Automorphism groups computed for specific examples
Abstract
We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of certain twisted tensor products. We employ our formulas to compute automorphism groups for examples in each case.
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