Group representations and construction of minimal topological groups

For every continuous biadditive mapping ω we construct a topological group M(ω) and establish its minimality under natural restrictions. Using the evaluation mapping G × G∗ → T of Pontryagin-van Kampen duality and the canonical duality E × E∗ → R for a normed space E, we obtain some new results in the theory of minimal groups. In particular, it is shown that every locally compact Abelian group is a group retract of a minimal locally compact group. Every Abelian topological group is a quotient of a perfectly minimal group.