Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups

DOI10.1134/S0040577917010019zbMath1432.17024arXiv1505.04612OpenAlexW2963557316WikidataQ115248200 ScholiaQ115248200MaRDI QIDQ682336

J. Abedi-Fardad, A. Rezaei-Aghdam, Ghorbanali Haghighatdoost

Publication date: 14 February 2018

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.04612

zbMATH Keywords

integrable systemLie bialgebraPoisson-Lie groupclassical \(r\)-matrix

Mathematics Subject Classification ID

Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Lie bialgebras; Lie coalgebras (17B62)

Related Items (4)

Invariant Poisson–Nijenhuis structures on Lie groups and classification ⋮ Unnamed Item ⋮ Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups ⋮ Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups

Cites Work

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• On the classical Young-Baxter equation for simple Lie algebras
• What is a classical r-matrix?
• Four dimensional symplectic Lie algebras
• Integrability of nonlinear systems. Proceedings of the CIMPA school, Pondicherry Univ., India, January 8--26, 1996
• \(N=2\) structures on solvable Lie algebras: The \(c=9\) classification
• Classical Yang-Baxter equation and low-dimensional triangular Lie bialgebras
• Classification of three-dimensional Lie bialgebras
• Complex and bi-Hermitian structures on four-dimensional real Lie algebras
• Invariants of real low dimension Lie algebras
• Classification of real three-dimensional Lie bialgebras and their Poisson–Lie groups
• CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES
• Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems
• Classification of two and three dimensional Lie superbialgebras
• Quantum groups
• Poisson-Lie \(T\)-duality and Bianchi type algebras

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