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

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• 作者：J. Abedi-Fardad ; A. Rezaei-Aghdam…
• 关键词：Lie bialgebra ; Poisson–Lie group ; classical r ; matrix ; integrable system
• 刊名：Theoretical and Mathematical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：190
• 期：1
• 页码：1-17
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Applications of Mathematics;
• 出版者：Pleiades Publishing
• ISSN：1573-9333
• 卷排序：190

文摘

We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson–Lie groups. We obtain some new integrable models where a Poisson–Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.