Classification of real three-dimensional Poisson-Lie groups

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.

arXiv comment25 pages

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Cited by in corpus (4)

• On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Quantizations of D=3 Lorentz symmetry
• Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras