Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras
Differential Geometry
2016-01-12 v2
Abstract
We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our construction is equivalent to that of fusion products of quasi-Poisson G-manifolds introduced by Alekseev, Kosmann- Schwarzbach, and Meinrenken. Our primary examples include four series of holomorphic Poisson structures on products of flag varieties and related spaces of complex semi-simple Lie groups.
Keywords
Cite
@article{arxiv.1504.06843,
title = {Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras},
author = {Jiang-Hua Lu and Victor Mouquin},
journal= {arXiv preprint arXiv:1504.06843},
year = {2016}
}
Comments
37 pages, submitted to IMRN