When unit groups of continuous inverse algebras are regular Lie groups

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

Studia Mathematica, Tome 211 (2012) no. 2, pp. 95-109

Résumé

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.

Détail

DOI : 10.4064/sm211-2-1

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