Inhomogeneous quantum groups related to two-dimensional quantum planes

Abstract

We propose a simple and compact method for deriving quantum groups acting on Manin's q- and h-planes. Using this method, we classify all the rigid motions of the two-dimensional quantum planes. Requiring that these inhomogenous transformations preserve differential structure of the quantum plane, we obtain two distinct inhomogenous quantum groups for the q-plane and one previously unknown inhomogenous quantum group for the h-plane, IGLh,h'(2).