On interpretations and constructions of classical dynamical r-matrices

Abstract

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.

8 pages, LaTeX, based on a talk given by L.F. at the QTS2 symposium, 18-21 July 2001, Krakow, Poland. References are updated, and a typo is removed in v2; a misprint in equation (A.13) is corrected in v3

Cited by in corpus (2)

• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Dynamical r-matrices and Poisson-Lie symmetries in the chiral WZNW model