Classification of real three-dimensional Poisson-Lie groups

Details Classification of real three-dimensional Poisson-Lie groups Classification of real three-dimensional Poisson-Lie groups

2012-02-09

arxiv.org/abs/1202.2077v1

Physics

Mathematical Physics

25 pages

Scientific paper

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.

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