Quantum orbits of the R-matrix type

J. Donin, D. Gurevich

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Given a simple Lie algebra g, we consider the orbits in g* which are of the 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 the 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.

Original languageEnglish
Pages (from-to)263-276
Number of pages14
JournalLetters in Mathematical Physics
Issue number3
StatePublished - Nov 1995


  • Mathematics Subject Classifications (1991): 17B37, 16W30


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