Quantum Clifford algebras from spinor representations
- Instituto de Matematicas, U.N.A.M., Circuito Exterior, C.U., Mexico, D.F. C.P. 04510 (Mexico)
- Instituto de Ciencias Nucleares, U.N.A.M., Ap. Postal 70-543, Mexico, D.F. C.P. 04510 (Mexico)
A general theory of quantum Clifford algebras is presented, based on a quantum generalization of the Cartan theory of spinors. We concentrate on the case when it is possible to apply the quantum-group formalism of bicovariant bimodules. The general theory is then singularized to the quantum SL({ital n},{bold C}) group case, to generate explicit forms for the whole class of braidings required. The corresponding spinor representations are introduced and investigated. Starting from our Clifford algebras we introduce the quantum-Euclidean underlying spaces compatible with different choices of {asterisk}-structures from where the analogues of Dirac and Laplace operators are built. Using the formalism developed, quantum Spin({ital n}) groups are defined. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 392126
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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