On dynamical \(r\)-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras (Q2766242)

The authors show that Dirac reduction of certain Poisson manifolds give rise to a mapping from dynamical \(r\)-matrices on a pair \(\mathcal{L}\subset\mathcal{A}\) to those on another pair \(\mathcal{K}\subset\mathcal{A}\), where \(\mathcal{K}\subset\mathcal{L}\subset\mathcal{A}\) is a chain of Lie algebras for which \(\mathcal{L}\) admits a reductive decomposition as \(\mathcal{L}=\mathcal{K}\oplus\mathcal{M}\). The authors show also that several known \(r\)-matrices appear naturally in this setting, and that it also can be applied to produce new \(r\)-matrices. Finally, the authors describe several series of \(r\)-matrices associated with self-dual Lie algebras.