Abstract: We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential calculi are known on it. More precisely, we describe how to construct in a Cartan `moving-frame formalism' the metric, two covariant derivatives, the Dirac operator, the frame, the inner derivations dual to the frame elements, for both of these calculi. The components of the frame elements in the basis of differentials provide a `local realization' of the Faddeev-Reshetikhin-Takhtadjan generators of $U_q^{\pm}(so(N))$.
Geometrical Techniques for the N-dimensional Quantum Euclidean Spaces / B. L., Cerchiai; Fiore, Gaetano; J., Madore. - STAMPA. - 2:(2002), pp. 663-673. ( VI Wigner Symposium Istanbul, Turchia agosto 1999).
Geometrical Techniques for the N-dimensional Quantum Euclidean Spaces
FIORE, GAETANO;
2002
Abstract
Abstract: We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential calculi are known on it. More precisely, we describe how to construct in a Cartan `moving-frame formalism' the metric, two covariant derivatives, the Dirac operator, the frame, the inner derivations dual to the frame elements, for both of these calculi. The components of the frame elements in the basis of differentials provide a `local realization' of the Faddeev-Reshetikhin-Takhtadjan generators of $U_q^{\pm}(so(N))$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
