Linear Connections on the Two Parameter Quantum Plane

Abstract

We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there exists a non trivial family of linear connections only when the two parameters obeys a specific relation.

7 pages, TeX

References in corpus (1)

• Connections on central bimodules

Cited by in corpus (7)

• Gauge theories on quantum spaces
• Noncommutative Geometry of the h-deformed Quantum Plane
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• Automorphisms of associative algebras and noncommutative geometry
• Differential geometry of GL${}_h(1|1)$
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects