论文标题
在多项式代数和laurent多项式代数上的广义Weyl代数的生长
Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras
论文作者
论文摘要
我们主要研究广义Weyl代数（GWA）$ A = D（σ，A）$ d $是多项式代数或laurent tolurent polynomial代数的广义Weyl代数（GWA）$ a = D（σ，A）的生长和Gelfand-Kirillov维度（GK-Dimension）。给出了$ \ operatoTorname {gkdim}（a）= \ operatatorName {gkdim}（d）+1 $的几个必要且充分的条件。特别是，我们证明了在两种不确定的多项式代数上GWA的GK-Dimension的二分法，即，在这种情况下，$ \ operatatOrName {gkdim}（a）$是$ 3 $或$ \ infty $。我们的结果概括了文献中的几个，并且可以应用于确定某些GWAS的生长，GK维度，简单性和取消特性。
We mainly study the growth and Gelfand-Kirillov dimension (GK-dimension) of 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 $\operatorname{GKdim}(A)=\operatorname{GKdim}(D)+1$ are given. In particular, we prove a dichotomy of the GK-dimension of GWAs over the polynomial algebra in two indeterminates, namely, $\operatorname{GKdim}(A)$ is either $3$ or $\infty$ in this case. Our results generalize several ones in the literature and can be applied to determine the growth, GK-dimension, simplicity, and cancellation properties of some GWAs.
