经典杨-巴克斯特方程的解与非对易变形
Solutions of the classical Yang-Baxter equation and noncommutative deformations
摘要：
在本文中，我将证明，如果一个李代数$\G$作用在一个流形$P$上，经典的杨-巴克斯特方程在$\G$上的任何解决方案给出了一个泊松张量在$P$和一个无挠和平坦的逆变联系（关于泊松张量）。而且，如果作用是局部自由的，则上述逆变联络的亚曲率为零。这将允许得到一大类满足Hawkins在Math.QA/0504232中提出的非对易变形存在的必要条件的流形。
英文摘要：
In this paper, I will show that, if a Lie algebra $\G$ acts on a manifold $P$, any solution of the classical Yang-Baxter equation on $\G$ gives arise to a Poisson tensor on $P$ and a torsion-free and flat contravariant connection (with respect to the Poisson tensor). Moreover, if the action is locally free, the matacurvature of the above contravariant connection vanishes. This will permit to get a large class of manifolds which satisfy the necessary conditions, presented by Hawkins in math.QA/0504232, to the existence of a noncommutative deformation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
