dorsal/arxiv
View SchemaQuantum and braided group Riemannian geometry
| Authors | S. Majid |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709025 |
| URL | https://arxiv.org/abs/q-alg/9709025 |
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 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 examples, including quantum spheres and quantum planes.
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"abstract": "We formulate quantum group Riemannian geometry as a gauge theory of quantum\ndifferential forms. We first develop (and slightly generalise) classical\nRiemannian geometry in a self-dual manner as a principal bundle frame\nresolution and a dual pair of canonical forms. The role of Levi-Civita\nconnection is naturally generalised to connections with vanishing torsion and\ncotorsion, which we introduce. We then provide the corresponding quantum group\nand braided group formulations with the universal quantum differential\ncalculus. We also give general constructions for examples, including quantum\nspheres and quantum planes.",
"arxiv_id": "q-alg/9709025",
"authors": [
"S. Majid"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Quantum and braided group Riemannian geometry",
"url": "https://arxiv.org/abs/q-alg/9709025"
},
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