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

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

1999-10-29

arxiv.org/abs/math/9910173v1

Communications in Algebra,27(9), 4307-4325 (1999)

Mathematics

Quantum Algebra

22 pages, 4 figures, LaTex2e

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-240770