On the double normalizer of the stable subalgebra of a plesiocompact homogeneous space

The class contains all compact homogeneous spaces as well as homogeneous spaces admitting a finite invariant measure. In the present article, a natural subalgebra is considered which contains the stable subalgebra of a plesiocompact homogeneous space. Its properties and structure are investigated. The analogous results are established on the level of Lie groups. This enables one to approach the problem of describing arbitrary plesiocompact homogeneous spaces from the new stand outlined in the article.