Classification of three-dimensional Lie bialgebras

DOI10.1063/1.533385zbMath0976.17012OpenAlexW1966639267MaRDI QIDQ2738090

Xavier Gomez

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.533385

zbMATH Keywords

classificationDrinfeld doubles3-dimensional Lie algebras3-dimensional Lie bialgebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Lie bialgebras; Lie coalgebras (17B62)

Related Items (15)

CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES ⋮ Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems ⋮ Towards \((3+1)\) gravity through Drinfel'd doubles with cosmological constant ⋮ LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS ⋮ AdS Poisson homogeneous spaces and Drinfel’d doubles ⋮ Poisson-Lie T-plurality revisited. Is T-duality unique? ⋮ Poisson–Hopf algebra deformations of Lie–Hamilton systems ⋮ A construction of Lie bialgebras from Lie coalgebras via antisymmetric bilinear forms ⋮ Curvature from quantum deformations ⋮ Unnamed Item ⋮ Poisson–Lie groups, bi-Hamiltonian systems and integrable deformations ⋮ Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups ⋮ The Poincaré group as a Drinfel’d double ⋮ Drinfel’d superdoubles and Poisson–Lie T-plurality in low dimensions ⋮ Classification of two and three dimensional Lie superbialgebras

Cites Work

• Analytic classification of pairs of involutions and its applications
• Manin pairs and topological conformal field theory
• Boundary solutions of the classical Yang-Baxter equation
• Biquantization of Lie bialgebras.
• \(N=2\) structures on solvable Lie algebras: The \(c=9\) classification
• Quantization of Lie bialgebras. I
• On frobenius lie algebras
• QuantumE(2) groups and Lie bialgebra structures
• Poisson-Lie \(T\)-duality for quasitriangular Lie bialgebras

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