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On The non-commutative Riemannian geometry of GL_q(n)

Y. Georgelin·J. Madore·T. Masson·J. Mourad
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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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BibTeXRIS

Y. Georgelin, J. Madore, T. Masson, J. Mourad. 1995-07-06. On The non-commutative Riemannian geometry of GL_q(n). https://arxiv.org/abs/q-alg/9507002

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