24 research outputs found
Frame formalism for the N-dimensional quantum Euclidean spaces
We sketch our recent application of a non-commutative version of the Cartan
`moving-frame' formalism to the quantum Euclidean space , the space
which is covariant under the action of the quantum group . For each of
the two covariant differential calculi over based on the -matrix
formalism, we summarize our construction of a frame, the dual inner
derivations, a metric and two torsion-free almost metric compatible covariant
derivatives with a vanishing curvature. To obtain these results we have
developed a technique which fully exploits the quantum group covariance of
. We first find a frame in the larger algebra \Omega^*(R^N_q) \cocross
\uqs. Then we define homomorphisms from R^N_q \cocross U_q^{\pm}{so(N)} to
which we use to project this frame in .Comment: Latex file, 11 pages. Talks given at the Euroconference
``Non-commutative Geometry and Hopf Algebras in Field Theory and Particle
Physics'', Villa Gualino (Torino), Sept. 199