Fundamentals of direct limit Lie theory
Group Theory
2007-05-23 v2
Abstract
We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of finite-dimensional Lie theory to the case of direct limit groups. In particular, we obtain an analogue of Lie's third theorem: Every countable-dimensional real or complex locally finite Lie algebra is enlargible, i.e., it is the Lie algebra of some regular Lie group (a suitable direct limit group).
Keywords
Cite
@article{arxiv.math/0403093,
title = {Fundamentals of direct limit Lie theory},
author = {Helge Glockner},
journal= {arXiv preprint arXiv:math/0403093},
year = {2007}
}
Comments
33 pages (v2: Lemma 7.12 and Proposition 7.13 corrected, clearer distinction between analyticity and convenient analyticity)