Linear connections on the quantum plane

Michel Dubois-Violette (1) , John Madore (1) , Thierry Masson (1) , Jihad Mourad (1)

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

A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.

Domaines: Algèbres quantiques [math.QA]; Physique des Hautes Energies - Théorie [hep-th]

Michel Dubois-Violette, John Madore, Thierry Masson, Jihad Mourad. Linear connections on the quantum plane. Letters in Mathematical Physics, 1995, 35, pp.351-358. ⟨hal-00013532⟩