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

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arxiv math-ph/0412092 v2 pith:DYOTBRYT submitted 2004-12-26 math-ph math.MP

A. Rezaei-Aghdam , M. Hemmati , A.R. Rastkar This is my paper · ORCID
classification math-phmath.MP
keywords bialgebrasrealthree-dimensionalgroupsobtainedpoisson-liebracketclassical
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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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  1. Classification of Six-dimensional Real Nilpotent Lie Bialgebras of Symplectic Type and their Poisson-Lie Groups

    math-ph 2026-07 reject novelty 4.0 of 10

    A claimed complete classification of six-dimensional nilpotent symplectic-type Lie bialgebras, presented as tables with only one worked derivation and with internal inconsistencies in the Poisson-bracket and applicati...

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