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

Journal Article · Tue Dec 15 00:00:00 EST 1998 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.57119· OSTI ID:21202692

Coquereaux, R; Schieber, G E ^[1]

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1. Centre de Physique Theorique, CNRS, Luminy, Case 907, F-13288 Marseille Cedex 9 (France)

Using the fact that the algebra MxM{sub 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{sub 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.

• OSTI ID: 21202692
• Journal Information: AIP Conference Proceedings, Vol. 453, Issue 1; Conference: Conference on particles, fields and gravitation, Lodz (Poland), 15-19 Apr 1998; Other Information: DOI: 10.1063/1.57119; (c) 1998 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
MATRICES
NONLINEAR PROBLEMS
QUANTUM FIELD THEORY
QUANTUM GROUPS
SL GROUPS
SPACE
SYMMETRY