Physics – Mathematical Physics
Scientific paper
2001-05-30
J.Phys. A34 (2001) 7235-7248
Physics
Mathematical Physics
19 pages, LaTeX, added a reference and a footnote and removed some typos
Scientific paper
10.1088/0305-4470/34/36/313
According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair $\L\subset \A$ to those on another pair $\K\subset \A$, where $\K\subset \L\subset \A$ is a chain of Lie algebras for which $\L$ admits a reductive decomposition as $\L=\K+\M$. Several known dynamical r-matrices appear naturally in this setting, and its application provides new r-matrices, too. In particular, we exhibit a family of r-matrices for which the dynamical variable lies in the grade zero subalgebra of an extended affine Lie algebra obtained from a twisted loop algebra based on an arbitrary finite dimensional self-dual Lie algebra.
Feher Laszlo
Gabor András
Pusztai B. G.
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