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 U g into a quantum group (or into a triangular Hopf algebra) U q g, i.e., so as to remain covariant under the action of U q g. 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 intriguing 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.
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Fiore, G. (2000). On q-Deformations of Clifford Algebras. In: Abłamowicz, R., Fauser, B. (eds) Clifford Algebras and their Applications in Mathematical Physics. Progress in Physics, vol 18. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1368-0_14
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DOI: https://doi.org/10.1007/978-1-4612-1368-0_14
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