论文标题
平面谎言代数的三角形结构
Triangular structures on flat Lie algebras
论文作者
论文摘要
在这项工作中，我们研究了一大批精确的libe骨，这是由托有左不变的riemannian指标的泊松族群体的非交换变形引起的。我们称这些结构为\ emph {精确的元fla lie bialgebras}。我们对这些结构进行完整的分类。我们表明，鉴于元曲折的几何条件，这些精确的双齿结构必然来自经典杨巴克斯特方程的非平凡溶液。此外，双重谎言的bialgebra也是平坦的，并且构成了一种重要的对称性。
In this work we study a large class of exact Lie bialgebras arising from noncommutative deformations of Poisson-Lie groups endowed with a left invariant Riemannian metric. We call these structures \emph{exact metaflat Lie bialgebras}. We give a complete classification of these structures. We show that given the metaflatness geometrical condition, these exact bialgebra structures arise necessarily from a nontrivial solution of the classical Yang-Baxter equation. Moreover, the dual Lie bialgebra is also flat and metaflat constituting an important kind of symmetry.
