We associate a dynamical r-matrix with any such subalgebra ℒ of a finite dimensional self-dual Lie algebra A for which the scalar product of A remains nondegenerate on ℒ and there exists a nonempty open subset ℒ̌ ⊂ ℒ so that the restriction of (ad λ) ∈ End (A) to ℒ⊥ is invertible ∀λ ∈ ℒ̌. This r-matrix is also well-defined if ℒ is the grade zero subalgebra of an affine Lie algebra A obtained from a twisted loop algebra based on a finite dimensional self-dual Lie algebra script G sign. Application of evaluation homomorphisms to the twisted loop algebras yields spectral parameter dependent script G sign ⊗ script G sign-valued dynamical r-matrices that are generalizations of Felder's elliptic r-matrices.
ASJC Scopus subject areas
- Physics and Astronomy(all)