On continuous cohomology of locally compact Abelian groups and bilinear maps

Let A be an abelian topological group and B a trivial topological A-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can be embedded in the second bilinear cohomology.

On continuous cohomology of locally compact Abelian groups and bilinear maps Keywords:

Bilinear cohomology , central extension , nilpotent of class two