On q-Deformations of Clifford Algebras

Abstract

Several Clifford algebras that are covariant under the action of a Lie algebra $g$ can be deformed in a way consistent with the deformation of $Ug$ into a quantum group (or into a triangular Hopf algebra) $U_qg$, i.e. so as to remain covariant under the action of $U_qg$. In this report, after recalling these facts, we review our results regarding the formal realization of the elements of such ``q-deformed'' Clifford algebras as ``functions'' (polynomials) in the generators of the undeformed ones; in particular, the intruiging interplay between the original and the q-deformed symmetry. Finally, we briefly illustrate their dramatic consequences on the representation theories of the original and of the q-deformed Clifford algebra, and mention how these results could turn out to be useful in quantum physics.

14 pages, LaTex. To appear in Proceedings of the 5th International Conference on Clifford Algebras, Ixtapa 1999