Some aspects of noncommutative differential geometry

Michel Dubois-Violette (1)

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

We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a general theory of connections in this framework.

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

Michel Dubois-Violette. Some aspects of noncommutative differential geometry. Contemporary mathematics, 1997, 203, pp.143-157. ⟨hal-00013528⟩