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

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

1999-10-19

arxiv.org/abs/math/9910095v1

Communications in Algebra, 27(4),1843-1878(1999)

Mathematics

Quantum Algebra

35 pages, LaTex2e

Scientific paper

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.

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