Discriminant formulas and applications

Chan, Kenneth; Young, Alexander; Zhang, James

doi:10.2140/ant.2016.10.557

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Discriminant formulas and applications

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

Vol. 10 (2016), No. 3, 557–596

DOI: 10.2140/ant.2016.10.557

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

Vol. 10, No. 3, 2016