Quantum Orbits of R-matrix Type
نویسندگان
چکیده
Given a simple Lie algebra g, we consider the orbits in g * which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of R-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pencil on these orbits in a similar way. The notions of q-deformed Lie brackets, braided coadjoint vector fields and tangent vector fields are discussed as well.
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