论文标题
由经典Yang-baxter方程定义的Lie Bialgebras的代数几何形状
Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
论文作者
论文摘要
本文致力于无限尺寸谎言双gebras的代数几何研究，这是由经典的杨巴克斯特方程解决方案产生的。我们将该方程式的三角解决方案视为标准lie Bialgebra Cobracket在适当的仿射谎言代数上的曲折，并阐明了Manin Triples的相应理论，将其置于代数几何环境中。由于这种方法，我们证明了经典Yang-baxter方程的任何三角解。一些具体的例子说明了开发的理论。
This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang-Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang-Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples.
