Module algebra structures of nonstandard quantum group $X_{q}(A_{1})$ on $\C_{q}[x,y,z]$

Abstract

In this paper, the module algebra structures of $X_{q}(A_{1})$ on quantum polynomial algebra $\C_{q}[x,y,z]$ are investigated, and a complete classification of $X_{q}(A_{1})$-module algebra structures on $\C_{q}[x,y,z]$ is given