Zariski Cancellation Problem for Noncommutative Algebras

2016/01/18 by Bell, Jason, Zhang, James J. · 2 citations
#16S38 #16W25 #16W70 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1601.04625

Abstract

A noncommutative analogue of the Zariski cancellation problem asks whether A[x]≅ B[x] implies A≅ B when A and B are noncommutative algebras. We resolve this affirmatively in the case when A is a noncommutative finitely generated domain over the complex field of Gelfand-Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin-Schelter regular algebras of higher Gelfand-Kirillov dimension.

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• Cancellation problem via locally nilpotent derivations
• Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras

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