Action of a finite quantum group on the algebra of complex NxN matrices

Details Action of a finite quantum group on the algebra of complex NxN matrices Action of a finite quantum group on the algebra of complex NxN matrices

1998-07-15

arxiv.org/abs/math-ph/9807016v1

AIP Conf.Proc. 453 (1998) 9-23

Physics

Mathematical Physics

11 pages, LaTeX, uses diagrams.sty, to be published in "Particles, Fields and Gravitation" (Lodz conference), AIP proceedings

Scientific paper

10.1063/1.57119

Using the fact that the algebra M := M_N(C) of NxN complex matrices can be considered as a reduced quantum plane, and that it is a module algebra for a finite dimensional Hopf algebra quotient H of U_q(sl(2)) when q is a root of unity, we reduce this algebra M of matrices (assuming N odd) into indecomposable modules for H. We also show how the same finite dimensional quantum group acts on the space of generalized differential forms defined as the reduced Wess Zumino complex associated with the algebra M.

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