Levi-Civita Connections on the Quantum Groups SL_q(N), O_q(N) and Sp_q(N)

1995/12/01 by Heckenberger, I., Schmuedgen, K. · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9512001

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 SL_q(N), O_q(N) and Sp_q(N) from the classification of Schmuedgen, K. and Schueler, A. there exist unique Levi-Civita connections.

Cited by

• On two notions of torsion and metric compatibility of connections in noncommutative geometry

Related

• Levi-Civita connection for SU_q(2)
• Metric compatibility and Levi-Civita Connections on Quantum Groups
• Classification of Bicovariant Differential Calculi on the Quantum Groups SL_q(n+1) and Sp_q(2n)
• Classification of Bicovariant Differential Calculi
• Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit