Double Lie algebras, semidirect product, and integrable systems
Mathematical Physics
2014-05-20 v1 High Energy Physics - Theory
math.MP
Abstract
We study integrable systems on double Lie algebras in absence of Ad-invariant bilinear form by passing to the semidirect product with the -representation. We show that in this stage a natural Ad-invariant bilinear form does exist, allowing for a straightforward application of the AKS theory, and giving rise to Manin triple structure, thus bringing the problem to the realm of Lie bialgebras and Poisson-Lie groups.
Keywords
Cite
@article{arxiv.1405.4340,
title = {Double Lie algebras, semidirect product, and integrable systems},
author = {S. Capriotti and H. Montani},
journal= {arXiv preprint arXiv:1405.4340},
year = {2014}
}