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Lie Groups of Measurable Mappings

Published online by Cambridge University Press:  20 November 2018

Helge Glöckner
Helge Glöckner*
Affiliation:
Technische Universität Darmstadt, Fachbereich Mathematik, AG 5, Schlossgartenstr. 7, 64289 Darmstadt, Germany email: [email protected]
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Abstract

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We describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space $\left( X,\,\sum ,\,\mu \right)$ and (possibly infinite-dimensional) Lie group $G$, we construct a Lie group ${{L}^{\infty }}\left( X,G \right)$, which is a Fréchet-Lie group if $G$ is so. We also show that the weak direct product $\prod{_{i\in I}^{*}{{G}_{i}}}$ of an arbitrary family ${{\left( {{G}_{i}} \right)}_{i\in I}}$ of Lie groups can be made a Lie group, modelled on the locally convex direct sum ${{\oplus }_{i\in I}}L\left( {{G}_{i}} \right)$ .

Keywords

Primary:22E65secondary:46E4046E3022E6746T2046T25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 5 , 01 October 2003 , pp. 969 - 999
Copyright
Copyright © Canadian Mathematical Society 2003

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