Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups

Details Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups

2004-12-26

arxiv.org/abs/math-ph/0412092v2

J.Phys.A: Math. Gen. 38(2005)3981-3994

Physics

Mathematical Physics

17 pages

Scientific paper

10.1088/0305-4470/38/18/008

Classical r-matrices of the three-dimensional real Lie bialgebras are
obtained. In this way all three-dimensional real coboundary Lie bialgebras and
their types (triangular, quasitriangular or factorizable) are classified. Then,
by using the Sklyanin bracket, the Poisson structures on the related
Poisson-Lie groups are obtained.

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