Generalizations of Felder's elliptic dynamical r-matrices associated with twisted loop algebras of self-dual Lie algebras

L. Fehér, B. G. Pusztai

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A dynamical r-matrix is associated with every self-dual Lie algebra A which is graded by finite-dimensional subspaces as A = ⊕n∈ZAn, where An is dual to A-n with respect to the invariant scalar product on A, and A0 admits a nonempty open subset A0 for which ad κ is invertible on An if n ≠ 0 and κ ∈ Ǎ0. Examples are furnished by taking A to be an affine Lie algebra obtained from the central extension of a twisted loop algebra ℓ(G, μ) of a finite-dimensional self-dual Lie algebra G. These r-matrices, R: Ǎ0 → End(A), yield generalizations of the basic trigonometric dynamical r-matrices that, according to Etingof and Varchenko, are associated with the Coxeter automorphisms of the simple Lie algebras, and are related to Felder's elliptic r-matrices by evaluation homomorphisms of ℓ(G, μ) into G. The spectral-parameter-dependent dynamical r-matrix that corresponds analogously to an arbitrary scalar-product-preserving finite order automorphism of a self-dual Lie algebra is here calculated explicitly.

Original languageEnglish
Pages (from-to)622-642
Number of pages21
JournalNuclear Physics B
Volume621
Issue number3
DOIs
Publication statusPublished - Jan 21 2002

Keywords

  • Classical Yang-Baxter equation
  • Dynamical r-matrix
  • Self-dual Lie algebra

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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