Generalization of the $h$-Deformation to Higher Dimensions

Abstract

In this article we construct $GL_{h}(3)$ from $GL_{q}(3)$ by a singular map. We show that there exist two singular maps which map $GL_{q}(3)$ to new quantum groups. We also construct their $R$-matrices and will show although the maps are singular but their $R$-matrices are not. Then we generalize these singular maps to the case $GL(N)$ and for $C_{n}$ series.