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

Kharchenko, V. K.; Keller, Jaime; Rodriguez-Romo, S.

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

Authors

Kharchenko, V. K.

Keller, Jaime

Rodriguez-Romo, S.

Description

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.
35 pages, LaTex2e