✦ LIBER ✦

Triangular Dynamical r-Matrices and Quantization

✍ Scribed by Ping Xu

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 329 KB
Volume: 166
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2000

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✦ Synopsis

We study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r: h g 0 M 2 g always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that nondegenerate 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 H 2 (g, h)Q(R.

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