Tensor representation of the quantum groupSL q (2,C) and quantum Minkowski space

We investigate the structure of the tensor product representation of the quantum groupSL _q (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 ofSL _q (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 groupSO _q(3, 1).