Frame, cotangent and tangent bundles of the quantum plane

Abstract

We construct a quantum frame bundle of the quantum plane $C_p^2$ by requiring that a $G{L}_{q,p}(2)$-covariant differential calculus on $C_p^2$ be isomorphic as a bimodule to the space of sections of the associated quantum cotangent bundle. We also construct the section space of the associated quantum tangent bundle, and show that it is naturally dual to the differential calculus.

8 pages, latex