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

L. Fehér, I. Marshall

Research output: Article

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 - okt. 1 2002

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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