摘要
利用H^3(RP^7)=0证明7维实射影空间RP^7不为Lie群,因此,RP^n为Lie群(或拓扑群)的充要条件是n=0,1,3。
The goal of this paper is to prove that 7-dimensional real projective space RP^7 is not a Lie group using H^3 RP^7)=0.Therefore, RP^n is a Lie group (or a topological group) if andonly if n =0,1, 3.
基金
Supported partially by TWAS and Chinese Science Fund
关键词
射影空间
LIE群
可平行流形
拓扑群
Lie group
topological group
parallelizable manifold
invariant differential form
