Vol. 10, No. 3, 2016

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Discriminant formulas and applications

Kenneth Chan, Alexander A. Young and James J. Zhang

Vol. 10 (2016), No. 3, 557–596
Abstract

The discriminant is a classical invariant associated to algebras which are finite over their centers. It was shown recently by several authors that if the discriminant of A is “sufficiently nontrivial” then it can be used to answer some difficult questions about A. Two such questions are: What is the automorphism group of A? Is A Zariski cancellative?

We use the discriminant to study these questions for a class of (generalized) quantum Weyl algebras. Along the way, we give criteria for when such an algebra is finite over its center and prove two conjectures of Ceken, Wang, Palmieri and Zhang.

Keywords
discriminant, automorphism group, cancellation problem, quantum algebra, Clifford algebra, rings and algebras
Mathematical Subject Classification 2010
Primary: 16W20
Milestones
Received: 7 April 2015
Revised: 7 February 2016
Accepted: 10 March 2016
Published: 12 June 2016
Authors
Kenneth Chan
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States
Alexander A. Young
Department of Mathematics
DigiPen Institute of Technology
9931 Willows Road NE
Redmond, WA 98052
United States
James J. Zhang
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350
United States