Quantum orbits of theR-matrix type |
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Authors: | J Donin D Gurevich |
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Institution: | (1) Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Centre de Mathématiques, Ecole Polytechnique, F-91128 Palaiseau, France |
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Abstract: | Given a simple Lie algebra g, we consider the orbits in g* which are of theR-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-calledR-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of theR-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 ofq-deformed Lie brackets, braided coadjoint vector fields, and tangent vector fields are discussed as well. |
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Keywords: | 17B37 16W30 |
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