On Cohomology Theory for Topological Groups

Proceedings Mathematical Sciences

Arati S Khedekar²  C S Rajan¹ 

[1] $$;School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 00 00, India$$

关键词: Cohomology theory;    group extension;    locally compact groups;    Lie groups.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of the identity. We show that if 𝐺 and 𝐴 are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of 𝐺 by 𝐴.

【 授权许可】

Unknown