Displaying similar documents to “Groups of diffeomorphisms and Lie theory.”

Varieties of topological groups, Lie groups and SIN-groups

Karl Hofmann, Sidney Morris, Markus Stroppel (1996)

Colloquium Mathematicae

Similarity:

In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups

A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś, Sławomir Turek (2011)

Open Mathematics

Similarity:

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.

An infinite dimensional version of the third Lie theorem

Rybicki, Tomasz

Similarity:

The concept of evolution operator is used to introduce a weak Lie subgroup of a regular Lie group, and to give a new version of the third Lie theorem. This enables the author to formulate and to study the problem of integrability of infinite-dimensional Lie algebras. Several interesting examples are presented.