TY - JOUR ID - 46 TI - On continuous cohomology of locally compact Abelian groups and bilinear maps JO - Journal of Algebra and Related Topics JA - JART LA - en SN - 2345-3931 AU - Sahleh, H. AD - University of Guilan Y1 - 2013 PY - 2013 VL - 1 IS - 1 SP - 67 EP - 77 KW - Bilinear cohomology KW - central extension KW - nilpotent of class two DO - N2 - 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. UR - https://jart.guilan.ac.ir/article_46.html L1 - https://jart.guilan.ac.ir/article_46_2de2cc9120ea26c74a54f5b4acc2febf.pdf ER -