On the noncommutative Riemannian geometry of GL(q)(n)

A recently proposed definition of a linear connection in noncommutative 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 permutations 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. (C) 1997 American Institute of Physics.