TENSOR REPRESENTATION OF THE QUANTUM GROUP SLQ(2,C) AND QUANTUM MINKOWSKI SPACE

We investigate the structure of the tensor product representation of the quantum group SLq(2,C) by using the 2-dimensional quantum plane as a building block. Two types of 4-dimensional spaces are constructed applying the methods used in twistor theory. We show that the 4-dimensional real representation of SLq(2,C) generates a consistent non-commutative algebra, and thus it provides a quantum deformation of Minkowski space. The transformation of this 4-dimensional space gives the quantum Lorentz group SOq(3, 1). © 1990 Springer-Verlag.