Quantum and braided group Riemannian geometry
Abstract
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 selfdual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of LeviCivita 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 examples, including quantum spheres and quantum planes.
 Publication:

eprint arXiv:qalg/9709025
 Pub Date:
 September 1997
 DOI:
 10.48550/arXiv.qalg/9709025
 arXiv:
 arXiv:qalg/9709025
 Bibcode:
 1997q.alg.....9025M
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 45 pages LATEX, some .eps figures in the appendix only