Dynamicalr-matrices on the affinizations of arbitrary self-dual Lie algebras

We associate a dynamicalr-matrix with any such subalgebraL of a finite dimensional self-dual Lie algebraA for which the scalar product ofA remains nondegenerate onL and there exists a nonempty open subsetĽ ⊂L so that the restriction of (ad λ)εEnd(A) toL is invertible ∨λεĽ. Thisr-matrix is also well-defined ifL is the grade zero subalgebra of an affine Lie algebraA obtained from a twisted loop algebra based on a finite dimensional self-dual Lie algebraG. Application of evaluation homomorphisms to the twisted loop algebras yields spectral parameter dependentG ⊗G-valued dynamicalr-matrices that are generalizations of Felder’s ellipticr-matrices. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. This work was supported in part by the Hungarian National Science Fund (OTKA) under T034170.