Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3)

Abstract

Following the method already developed for studying the actions of GL_q(2,C) on the Clifford algebra C(1,3) and its quantum invariants (Commun. in Algebra 27, 1843-1878(1999)), we study the action on C(1,3) of the quantum group GL_2 constructed by Dipper and Donkin. We are able of proving that there exists only two non-equivalent cases of actions with nontrivial "perturbation". The space of invariants are trivial in both cases. We also prove that each irreducible finite dimensional algebra representation of the quantum group GL_2, q^m\neq 1, is one dimensional. By studying the cases with zero "perturbation" we find that the cases with nonzero "perturbation" are the only ones with maximal possible dimension for the operator algebra \Re.