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      https://www.ias.ac.in/article/fulltext/pmsc/122/02/0221-0242

    • 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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