Classification of real three-dimensional Poisson-Lie groups
Mathematical Physics
2012-05-09 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
All real three dimensional Poisson-Lie groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the complete classification of real three-dimensional Lie bialgebras given in [X. Gomez, J. Math. Phys. vol. 41, p. 4939 (2000)]. Many of these 3D Poisson-Lie groups are non-coboundary structures, whose Poisson brackets are given here for the first time. Casimir functions for all three-dimensional PL groups are given, and some features of several PL structures are commented.
Keywords
Cite
@article{arxiv.1202.2077,
title = {Classification of real three-dimensional Poisson-Lie groups},
author = {Angel Ballesteros and Alfonso Blasco and Fabio Musso},
journal= {arXiv preprint arXiv:1202.2077},
year = {2012}
}
Comments
25 pages