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arXiv · hep-th/9411034

Quantum orbits of R-matrix type

J. Donin·D. Gurevich
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Abstract

Given a simple Lie algebra $\gggg$, we consider the orbits in $\gggg^*$ 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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J. Donin, D. Gurevich. 1994-11-04. Quantum orbits of R-matrix type. https://doi.org/10.1007/bf00761298

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