Cotangent and tangent modules on quantum orbits

Details Cotangent and tangent modules on quantum orbits Cotangent and tangent modules on quantum orbits

2000-05-11

arxiv.org/abs/math/0005109v1

Mathematics

Quantum Algebra

13 pages, Latex

Scientific paper

10.1142/S0217979200001850

Let $k(S^2_q)$ be the "coordinate ring" of a quantum sphere. We introduce the cotangent module on the quantum sphere as a one-sided $k(S^2_q)$-module and show that there is no Yang-Baxter type operator converting it into a $k(S^2_q)$-bimodule which would be a flatly deformed object w.r.t. its classical counterpart. This implies non-flatness of any covariant differential calculus on the quantum sphere making use of the Leibniz rule. Also, we introduce the cotangent and tangent modules on generic quantum orbits and discuss some related problems of "braided geometry".

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