Zariski cancellation problem for noncommutative algebras

被引：27
|
作者：
Bell, Jason [1 ]
Zhang, James J. [2 ]
机构：
[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada
[2] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA
来源：
SELECTA MATHEMATICA-NEW SERIES | 2017年 / 23卷 / 03期
基金：
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
Zariski cancellation problem; Noncommutative algebra; Effective and dominating discriminant; Locally nilpotent derivation; Skew polynomial ring; AUTOMORPHISM-GROUPS; DERIVATIONS; SURFACES; SPACE;
D O I：
10.1007/s00029-017-0317-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A noncommutative analogue of the Zariski cancellation problem asks whether A[x] congruent to B[x] implies A congruent to 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.
引用
收藏
页码：1709 / 1737
页数：29
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