ON THE NONCOMMUTATIVE RIEMANNIAN GEOMETRY OF GL(Q)(N)

A recently proposed definition of a linear connection in noncommutativ e geometry, based on a generalized permutation, is used to construct l inear connections on GL(q)(n). Restrictions on the generalized permuta tion arising from the stability of linear connections under involution are discussed. Candidates for generalized permutations on GL(q)(n) ar e found. It is shown that, for a given generalized permutation, there exists one and only one associated linear connection. Properties of th e linear connection are discussed, in particular its bicovariance, tor sion, and commutative limit. (C) 1997 American Institute of Physics.