TY - JOUR
T1 - Poisson Manifolds Associated with Group Actions and Classical Triangular r-Matrices
AU - Xu, Ping
PY - 1993/2/15
Y1 - 1993/2/15
N2 - Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure PΛ on P. For this new Poisson structure PΛ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of PΛ is also discussed.
AB - Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure PΛ on P. For this new Poisson structure PΛ, we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of PΛ is also discussed.
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U2 - 10.1006/jfan.1993.1031
DO - 10.1006/jfan.1993.1031
M3 - Article
AN - SCOPUS:22244488802
SN - 0022-1236
VL - 112
SP - 218
EP - 240
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -