Dynamical r-matrices on the affinizations of arbitrary self-dual Lie algebras

L. Fehér, B. G. Pusztai

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)1318-1324
Number of pages7
JournalCzechoslovak Journal of Physics
Volume51
Issue number12
DOIs
Publication statusPublished - Dec 1 2001

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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