Quantum and braided group Riemannian geometry - INSPIRE

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Quantum and braided group Riemannian geometry

S. Majid
(
- Cambridge U., DAMTP
)

1999

34 pages

Published in:

J.Geom.Phys. 30 (1999) 113-146

DOI:

10.1016/S0393-0440(98)00051-5

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Abstract: (Elsevier)

We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of Levi-Civita connection is naturally generalised to connections with vanishing torsion and cotorsion, which we introduce. We then provide the corresponding quantum group and braided group formulations with the universal quantum differential calculus. We also give general constructions, for example, including quantum spheres and quantum planes.

Quantum groups
81R50
17B37
Braided groups
Riemannian geometry
quantum group
braid group
gauge field theory
differential forms
geometry

References(38)

Figures(0)

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