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 -