TY - JOUR

T1 - On a poisson-lie analogue of the classical dynamical Yang-Baxter equation for self-dual Lie algebras

AU - Fehér, L.

AU - Marshall, I.

PY - 2002/10/1

Y1 - 2002/10/1

N2 - 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.

AB - 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.

KW - Classical dynamical Yang-Baxter equation

KW - Poisson-Lie groups and groupoids

KW - Self-dual Lie algebra, Wess-Zumino-Novikov-Witten model

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U2 - 10.1023/A:1021681826447

DO - 10.1023/A:1021681826447

M3 - Article

AN - SCOPUS:0041366830

VL - 62

SP - 51

EP - 62

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -