Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 43, Number 1 (2003), 1-26.
Direct limit Lie groups and manifolds
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.
J. Math. Kyoto Univ., Volume 43, Number 1 (2003), 1-26.
First available in Project Euclid: 14 August 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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