On dynamicalr-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras

L Fehér, A Gábor, B G Pusztai
2001 Journal of Physics A: Mathematical and General  
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 Ł⊂ to those on another pair ⊂, where ⊂Ł⊂ is a chain of Lie algebras for which Ł admits a reductive decomposition as Ł=+. Several known dynamical r-matrices appear naturally in this setting, and its
more » ... plication 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.
doi:10.1088/0305-4470/34/36/313 fatcat:xlodugulebde7ooabwsh3l62ta