On a poisson-lie analogue of the classical dynamical Yang-Baxter equation for self-dual Lie algebras

L. Fehér, I. Marshall

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We derive a generalization of the classical dynamical Yang-Baxter equation (CDYBE) on a self-dual Lie algebra G by replacing the cotangent bundle T*G in a geometric interpretation of this equation by its Poisson-Lie (PL) analogue associated with a factorizable constant r-matrix on G. The resulting PL-CDYBE, with variables in the Lie group G equipped with the Semenov-Tian-Shansky Poisson bracket based on the constant r-matrix, coincides with an equation that appeared in an earlier study of PL symmetries in the WZNW model. In addition to its new group theoretic interpretation, we present a self-contained analysis of those solutions of the PL-CDYBE that were found in the WZNW context and characterize them by means of a uniqueness result under a certain analyticity assumption.

Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalLetters in Mathematical Physics
Volume62
Issue number1
DOIs
Publication statusPublished - Oct 2002

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Yang-Baxter Equation
Lie Algebra
Siméon Denis Poisson
algebra
analogs
Analogue
R-matrix
Lie Symmetry
Cotangent Bundle
Poisson Bracket
Analyticity
uniqueness
brackets
matrices
Uniqueness
bundles
symmetry
Interpretation
Model

Keywords

  • Classical dynamical Yang-Baxter equation
  • Poisson-Lie groups and groupoids
  • Self-dual Lie algebra, Wess-Zumino-Novikov-Witten model

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

On a poisson-lie analogue of the classical dynamical Yang-Baxter equation for self-dual Lie algebras. / Fehér, L.; Marshall, I.

In: Letters in Mathematical Physics, Vol. 62, No. 1, 10.2002, p. 51-62.

Research output: Contribution to journalArticle

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