Metric On Quantum Spaes

Abstract

We introduce the analogue of the metric tensor in case of $q$-deformed differential calculus. We analyse the consequences of the existence of such metric, showing that this enforces severe restrictions on the parameters of the theory. We discuss in detail the examples of the Manin plane and the $q$-deformation of $SU(2)$. Finally we touch the topic of relations with the Connes' approach.

7 pages (LaTeX), preprint TPJU 14/93

References in corpus (2)

• Quantum Group Gauge Theory on Classical Spaces
• Higgs Mass and Noncommutative Geometry

Cited by in corpus (6)

• Gravity and Electromagnetism in Noncommutative Geometry
• Metrics and Pairs of Left and Right Connections on Bimodules
• Riemannian Geometry of a Discretized Circle and Torus
• Quantum Braided PoincarÉ Group
• Noncommutative differential geometry with higher order derivatives
• Field Theory on $q=-1$ Quantum Plane