Journal of Mathematics of Kyoto University

Direct limit Lie groups and manifolds

Helge Glöckner

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Abstract

We show that every countable strict directed system of finitedimensional Lie groups has a direct limit in the category of smooth Lie groups modelled on sequentially complete, locally convex spaces. Similar results are obtained for countable directed systems of finite-dimensional manifolds, and for countable directed systems of finite-dimensional Lie groups and manifolds over totally disconnected local fields. An uncountable strict directed system of finite-dimensional Lie groups has a direct limit in the category of Lie groups in the sense of convenient differential calculus, provided certain technical hypotheses are satisfied.

Article information

Source
J. Math. Kyoto Univ., Volume 43, Number 1 (2003), 1-26.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283739

Digital Object Identifier
doi:10.1215/kjm/1250283739

Mathematical Reviews number (MathSciNet)
MR2028699

Zentralblatt MATH identifier
1056.22013

Citation

Glöckner, Helge. Direct limit Lie groups and manifolds. J. Math. Kyoto Univ. 43 (2003), no. 1, 1--26. doi:10.1215/kjm/1250283739. https://projecteuclid.org/euclid.kjm/1250283739


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