It is a basic fact in infinite-dimensional Lie theory that the unit group $A^\times $ of a continuous inverse algebra $A$ is a Lie group. We describe criteria ensuring that the Lie group $A^\times $ is regular in Milnor's sense. Notably, $A^\times $ is regular if $A$ is Mackey-complete and locally m-convex.
Keywords:
basic infinite dimensional lie theory unit group times continuous inverse algebra lie group describe criteria ensuring lie group times regular milnors sense notably times regular mackey complete locally m convex
Affiliations des auteurs :
Helge Glöckner
1
;
Karl-Hermann Neeb
2
1
Universität Paderborn Institut für Mathematik Warburger Str. 100 33098 Paderborn, Germany
2
FAU Erlangen-Nürnberg Department Mathematik Cauerstr. 11 91058 Erlangen, Germany
@article{10_4064_sm211_2_1,
author = {Helge Gl\"ockner and Karl-Hermann Neeb},
title = {When unit groups of continuous inverse algebras
are regular {Lie} groups},
journal = {Studia Mathematica},
pages = {95--109},
year = {2012},
volume = {211},
number = {2},
doi = {10.4064/sm211-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm211-2-1/}
}
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AU - Karl-Hermann Neeb
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Helge Glöckner; Karl-Hermann Neeb. When unit groups of continuous inverse algebras
are regular Lie groups. Studia Mathematica, Tome 211 (2012) no. 2, pp. 95-109. doi: 10.4064/sm211-2-1
