Mathematics – Functional Analysis
Scientific paper
2012-01-05
Mathematics
Functional Analysis
Scientific paper
The paper develops the theory of topological radicals of Banach Lie algebras and studies the structure of Banach Lie algebras with sufficiently many Lie subalgebras of finite codimensions -- the intersection of all these subalgebras is zero. It is shown that the intersections of certain families of Lie subalgebras (closed Lie subalgebras of finite codimension, closed Lie ideals of finite codimension, closed maximal Lie subalgebras of finite codimension, closed maximal Lie ideals of finite codimension) correspond to different preradicals, and that these preradicals generate the same radical, the Frattini radical. The main attention is given to structural properties of Frattini-semisimple Banach Lie algebras and, in particular, to a new infinite-dimensional phenomenon associated with the strong Frattini preradical introduced in this paper. A constructive description of Frattini-free Banach Lie algebras is obtained.
Kissin Edward
Shulman Victor
Turovskii Yurii
No associations
LandOfFree
Topological radicals, IV. Frattini theory for Banach Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Topological radicals, IV. Frattini theory for Banach Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological radicals, IV. Frattini theory for Banach Lie algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-609352