Levi-Civita Connections on the Quantum Groups SL_{q}(N), O_{q}(N) and Sp_{q}(N)

Abstract

For bicovariant differential calculi on quantum groups various notions on connections and metrics (bicovariant connections, invariant metrics, the compatibility of a connection with a metric, Levi-Civita connections) are introduced and studied. It is proved that for the bicovariant differential calculi on $S{L}_q(N)$, $O_q(N)$ and $S{p}_q(N)$ from the classification of Schmuedgen, K. and Schueler, A. there exist unique Levi-Civita connections.

LaTeX2E, 20 pages; extended version, will appear in CMP

References in corpus (2)

• Connections on central bimodules
• Noncommutative Geometry of Finite Groups

Cited by in corpus (1)

• Quantum and braided group Riemannian geometry