Fundamentals of direct limit Lie theory

Details Fundamentals of direct limit Lie theory Fundamentals of direct limit Lie theory

2004-03-04

arxiv.org/abs/math/0403093v2

Mathematics

Group Theory

33 pages (v2: Lemma 7.12 and Proposition 7.13 corrected, clearer distinction between analyticity and convenient analyticity)

Scientific paper

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).

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