dorsal/arxiv
View SchemaOn The non-commutative Riemannian geometry of GL_q(n)
| Authors | Y. Georgelin, J. Madore, T. Masson, J. Mourad |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507002 |
| URL | https://arxiv.org/abs/q-alg/9507002 |
Abstract
A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the stability of linear connections under involution are discussed. Candidates for generalized permutation on GL_q(n) are found. It is shown that, for a given generalized permutation, there exists one and only one associated linear connection. Properties of the linear connection are discussed, in particular its bicovariance, torsion and commutative limit.
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"abstract": "A recently proposed definition of a linear connection in non-commutative\ngeometry, based on a generalized permutation, is used to construct linear\nconnections on GL_q(n). Restrictions on the generalized permutation arising\nfrom the stability of linear connections under involution are discussed.\nCandidates for generalized permutation on GL_q(n) are found. It is shown that,\nfor a given generalized permutation, there exists one and only one associated\nlinear connection. Properties of the linear connection are discussed, in\nparticular its bicovariance, torsion and commutative limit.",
"arxiv_id": "q-alg/9507002",
"authors": [
"Y. Georgelin",
"J. Madore",
"T. Masson",
"J. Mourad"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "On The non-commutative Riemannian geometry of GL_q(n)",
"url": "https://arxiv.org/abs/q-alg/9507002"
},
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