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

1995/07/06 by Y. Georgelin, Georgelin, Y., J. Madore +5
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9507002

20 pages, Latex

arxiv created 1995/07/06 · arxiv updated 2009/11/30

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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