On a decomposition of the second cohomology of an abelian topological group

Abstract

Let C be an abelian topological group ,A a trivial C-module.In this paper we show that the second cohomology of C with the 2-divisible coefficient is isomorphic to the direct sum of the second cohomology of a Lie ring c , whose underlying group is C, and the group of symmetric cocycles. Also there is an isomorphism between the categories of abelian topological groups of nilpotency class two,with a continuous section , and that of Lie rings of nilpotency class two. Mathematics Subject Classification: 22A05