具有双不变拟Riemann度量的Lie群

Lie Groups with a Bi-Invariant Pseudo-Riemannian Metric

本文讨论了其有双不变拟Riemann度量的Lie群及其等距变换群的一些性质,证明了:1)具有双不变拟Riemann度量的Lie群的等距变换群一定非单;2)具有双不变拟Riemann度量的Lie群半单的充要条件是其等距变换群半单且非单.

In this paper,the properties of Lie groups with a bi-invariant pseudo-Riemannian metric and their iso- metric transformation groups are discussed.It is proved that:1)Isometric transformation groups of Lie groups with bi-invariant pseudo-Riemannian metrics are non-simple.2)Lie group U with a bi-invariant pseu- do-Riemannian metric is semisimple if and only if its isometric transformation group is semisimple and non- simple.