Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras
نویسندگان
چکیده
We mainly study the growth and Gelfand-Kirillov dimension (GK-dimension) of generalized Weyl algebra (GWA) $A=D(\sigma,a)$ where $D$ is a polynomial or Laurent algebra. Several necessary sufficient conditions for $\operatorname{GKdim}(A)=\operatorname{GKdim}(D)+1$ are given. In particular, we prove dichotomy GK-dimension GWAs over in two indeterminates, namely, $\operatorname{GKdim}(A)$ either $3$ $\infty$ this case. Our results generalize several ones literature can be applied to determine growth, GK-dimension, simplicity, cancellation properties some GWAs.
منابع مشابه
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ژورنال
عنوان ژورنال: Science China-mathematics
سال: 2022
ISSN: ['1674-7283', '1869-1862']
DOI: https://doi.org/10.1007/s11425-022-1992-2