On Riemann Curvature in Noncommutative Geometry

M. Dubois-Violette (1) , J. Madore (1) , T. Masson (1) , J. Mourad (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra. The corresponding curvatures are also compared.

Domaines: Algèbres quantiques [math.QA]; Géométrie différentielle [math.DG]

M. Dubois-Violette, J. Madore, T. Masson, J. Mourad. On Riemann Curvature in Noncommutative Geometry. Journal of Mathematical Physics, 1996, 37, pp.4089-4102. ⟨hal-00013526⟩