Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Quantum Clifford algebras from spinor representations

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.531744· OSTI ID:392126
 [1];  [2];  [1]; ;  [2]
  1. Instituto de Matematicas, U.N.A.M., Circuito Exterior, C.U., Mexico, D.F. C.P. 04510 (Mexico)
  2. 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

Similar Records

Bilinear covariants and spinor fields duality in quantum Clifford algebras
Journal Article · Wed Oct 15 00:00:00 EDT 2014 · Journal of Mathematical Physics · OSTI ID:22305862

Octonionic representations of Clifford Algebras and triality
Journal Article · Sun Dec 31 23:00:00 EST 1995 · Foundations of Physics · OSTI ID:272752

The construction of spinors in geometric algebra
Journal Article · Wed Jun 01 00:00:00 EDT 2005 · Annals of Physics (New York) · OSTI ID:20690162