Topological radicals, IV. Frattini theory of Banach Lie algebras

TL;DR

This paper extends Frattini theory to Banach Lie algebras by developing topological radicals, exploring their constructions, and analyzing radicals related to finite codimension subalgebras and ideals in infinite-dimensional settings.

Contribution

It introduces a framework for topological radicals in Banach Lie algebras, generalizing finite-dimensional Frattini theory to infinite-dimensional cases.

Findings

Developed new topological radicals for Banach Lie algebras

Extended finite-dimensional Frattini theory to infinite-dimensional context

Analyzed radicals associated with subalgebras and ideals of finite codimension

Abstract

We develop the theory of topological radicals in Banach Lie algebras, consider various ways of constructing such radicals and study a family of (pre)radicals related to subalgebras and ideals of finite codimension in Banach Lie algebras. It extends to the infinite-dimensional case many results of the well known Frattini theory of Lie algebras.