Linear connections on the quantum plane
Michel Dubois-Violette, John Madore, Thierry Masson, Jihad Mourad
TL;DR
This paper establishes the uniqueness of a linear connection on the quantum plane within noncommutative geometry, while also demonstrating the absence of a compatible metric.
Contribution
It proves the existence and uniqueness of a linear connection on the quantum plane and shows that no metric exists in this setting.
Findings
Unique linear connection on the quantum plane
No compatible metric exists
Clarifies geometric structures in noncommutative geometry
Abstract
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.
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