TY - JOUR

T1 - Quantum orbits of the R-matrix type

AU - Donin, J.

AU - Gurevich, D.

PY - 1995/11

Y1 - 1995/11

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0010119020&partnerID=8YFLogxK

U2 - 10.1007/BF00761298

DO - 10.1007/BF00761298

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AN - SCOPUS:0010119020

SN - 0377-9017

VL - 35

SP - 263

EP - 276

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 3

ER -