关于Lorentz群的各类Lie子群

On the Lie Subgroups of the Lorentz Group

Lorentz群以及它的各类Lie子群,对双曲空间几何学的研究有着重要作用。本文除证明(6参数)Lorentz群G不存在5—参数Lie子群(定理4)外,我们给出了G的各类Lie子群的参数表示(定理1,2,3,5)。

The group of motions of the hyperbolic space H3 isisomorphic to the Lorentz group G with six parameters. In this paper, excepting the proof that G includes no Lie 5 -subgroup, we obtain still respectively the parametric representation of every kind of Lie subgroups of the Lorentz group G .