Extensions of locally compact groups
Institute of Mathematical Sciences, Chennai.
We first recall the basics about group theory and then introduce the ``Extension problem''. This relates to the second Cohomology groups. We discuss the solution for finite groups and topological groups Further, we define an explicit cohomology theory for locally compact groups based on locally continuous measurable cochains. The second cohomology group parametrizes all the locally split extensions. We apply the theory to Lie groups acting on abelian Lie groups We show that the corresponding extensions are Lie groups.