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Linear connections in non-commutative geometry
1995
Classical and quantum gravity
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of Ω^1. A special role is played by the extension to the framework of non-commutative geometry of the permutation of two copies of Ω^1. The construction of the linear connection as well as the definition of torsion and curvature is first proposed in the setting of the derivations based
doi:10.1088/0264-9381/12/4/007
fatcat:xar4k5yi2bg6pht6jrgyjmi6em