On cohomology theory for topological groups
Identifieur interne : 000159 ( Main/Merge ); précédent : 000158; suivant : 000160On cohomology theory for topological groups
Auteurs : Arati S. Khedekar [Inde] ; C S Rajan [Inde]Source :
- Proceedings - Mathematical Sciences [ 0253-4142 ] ; 2012-05-01.
English descriptors
Abstract
Abstract: 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.
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DOI: 10.1007/s12044-012-0067-6
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<front><div type="abstract" xml:lang="en">Abstract: 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.</div>
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