Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras Dedicated to Professor Yuqun Chen on the Occasion of His 65th Birthday  

作　　者：Xiangui Zhao 

机构地区：[1]School of Mathematics and Statistics,Huizhou University,Huizhou 516007,China

出　　处：《Science China Mathematics》2023年第5期887-906,共20页中国科学：数学（英文版）

基　　金：supported by Huizhou University(Grant Nos.hzu202001 and 2021JB022);the Guangdong Provincial Department of Education(Grant Nos.2020KTSCX145 and 2021ZDJS080)。

摘　　要：We study the growth and the Gelfand-Kirillov dimension(GK-dimension)of the generalized Weyl algebra(GWA)A=D(σ,a),where D is a polynomial algebra or a Laurent polynomial algebra.Several necessary and sufficient conditions for GKdim(A)=GKdim(D)+1 are given.In particular,we prove a dichotomy of the GK-dimension of GWAs over the polynomial algebra in two indeterminates,i.e.,GKdim(A)is either 3 or∞in this case.Our results generalize several existing results in the literature and can be applied to determine the growth,GK-dimension,simplicity and cancellation properties of some GWAs.

关 键 词：Gelfand-Kirillov dimension generalized Weyl algebra polynomial automorphism 

分 类 号：O15[理学—数学]