Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras

2001/10/30 by Eugene Karolinsky, Karolinsky, Eugene, Alexander Stolin +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0110319

LaTeX, 20 pages. We add a method that allows to get constant r-matrices from dynamical ones (see Appendix B)

arxiv created 2002/02/12 · arxiv updated 2009/11/30

Abstract

Jiang-Hua Lu showed that any dynamical r-matrix for the pair (g,u) naturally induces a Poisson homogeneous structure on G/U. She also proved that if g is complex simple, u is its Cartan subalgebra and r is quasitriangular, then this correspondence is in fact 1-1. In the present paper we find some general conditions under which the Lu correspondence is 1-1. Then we apply this result to describe all triangular Poisson homogeneous structures on G/U for a simple complex group G and its reductive subgroup U containing a Cartan subgroup.

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