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    • Keywords


      Cohomology theory; group extension; locally compact groups; Lie groups.

    • 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.

    • Author Affiliations


      Arati S Khedekar1 C S Rajan1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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