TY - JOUR

T1 - Triangular dynamical r-matrices and quantization

AU - Xu, Ping

N1 - Funding Information:
1Research partially supported by NSF grants DMS97-04391 and DMS00-72171.

PY - 2002/3/1

Y1 - 2002/3/1

N2 - We study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r: h* → ∧2 g always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate triangular dynamical r-matrices (i.e., those such that the corresponding Poisson manifolds are symplectic) are quantizable and that the quantization is classified by the relative Lie algebra cohomology H2(g, h) ℏ.

AB - We study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r: h* → ∧2 g always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate triangular dynamical r-matrices (i.e., those such that the corresponding Poisson manifolds are symplectic) are quantizable and that the quantization is classified by the relative Lie algebra cohomology H2(g, h) ℏ.

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U2 - 10.1006/aima.2001.2000

DO - 10.1006/aima.2001.2000

M3 - Article

AN - SCOPUS:0036497108

VL - 166

SP - 1

EP - 49

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -