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.