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Frame, cotangent and tangent bundles of the quantum plane

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arxiv math/9803127 v1 pith:2FBPXW5E submitted 1998-03-26 math.QA math-phmath.MP

classification math.QAmath-phmath.MP
keywords quantumbundleassociatedcalculusconstructcotangentdifferentialframe
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abstract

We construct a quantum frame bundle of the quantum plane $C^2_p$ by requiring that a $GL_{q,p}(2)$-covariant differential calculus on $C^2_p$ 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.

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  1. On quantum $G$-structures

    math.QA 2026-06 accept novelty 6.0 of 10

    A quantum G-structure, defined as a reduction of a quantum frame resolution, itself forms a quantum frame resolution under a covariant first-order differential calculus.

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