论文标题
关于谎言代数的Riemannian连接和半动物
On riemannian connections and semi-simplicity of a Lie algebra
论文作者
论文摘要
使用喷雾剂定义的几乎产品结构，我们提供了必要且充分的条件，以使消失的扭转与riemannian进行线性连接，并为可预测的矢量场的lie代数的半模拟性与喷雾剂通勤。我们显示了有限维谎言代数的半简化性与衍生理想及其代数的巧合，与代数的任何衍生物的内在性以及其相邻表示的半敏捷性。
Using a almost product structure defined by a spray, we give a necessary and sufficient condition, for a linear connection with vanishing torsion to be Riemannian and, for the semi-simplicity of Lie algebra of projectable vector fields which commute with a spray. We show the equivalence of the semi-simplicity of a finite dimensional Lie algebra to the coincidence of the derived ideal with its algebra, to the interiority of any derivation of the algebra and, to the semi-simplicity of its adjoint representation.
