On interpretations and constructions of classical dynamical r-matrices

Details On interpretations and constructions of classical dynamical r-matrices On interpretations and constructions of classical dynamical r-matrices

2001-11-28

arxiv.org/abs/hep-th/0111252v3

pp. 331-336 in: Quantum Theory and Symmetries, eds. E. Kapuscik et al, World Scientific, 2002

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, LaTeX, based on a talk given by L.F. at the QTS2 symposium, 18-21 July 2001, Krakow, Poland. References are updated,

Scientific paper

In this note we complement recent results on the exchange $r$-matrices appearing in the chiral WZNW model by providing a direct, purely finite-dimensional description of the relationship between the monodromy dependent 2-form that enters the chiral WZNW symplectic form and the exchange $r$-matrix that governs the corresponding Poisson brackets. We also develop the special case in which the exchange $r$-matrix becomes the `canonical' solution of the classical dynamical Yang-Baxter equation on an arbitrary self-dual Lie algebra.

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