Actions of GL_q(2,C) on C(1,3) and its four dimensional representations

Abstract

A complete classification is given of all inner actions on the Clifford algebra C(1,3) defined by representations of the quantum group GL_q(2,C), q^m\neq 1, which are not reduced to representations of two commuting "q-spinors". As a consequence of this classification it is shown that the space of invariants of every GL_q(2,C)-action of this type, which is not an action of SL_q(2,C), is generated by 1 and the value of the quantum determinant for the given representation.