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.
On q-deformed Clifford algebras / Fiore, Gaetano. - STAMPA. - (2000), pp. 269-282. (Intervento presentato al convegno 5th International Conference on Clifford Algebras tenutosi a Ixtapa-Zihuatanejo, Mexico nel giugno 1999).
On q-deformed Clifford algebras
FIORE, GAETANO
2000
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
