Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă ¹   ; Karl-Hermann Neeb ²

¹ Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 Bucureşti, Romania
² Department of Mathematics Darmstadt University of Technology Schlossgartenstrasse 7 D-64289 Darmstadt, Germany

Studia Mathematica, Tome 185 (2008) no. 3, pp. 249-262

Résumé

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute modulo the Jacobson radical.

Détail

DOI : 10.4064/sm185-3-3

Keywords: investigate finite dimensional lie groups whose points separated continuous homomorphisms groups invertible elements locally convex algebras continuous inversion satisfy appropriate completeness condition these precisely linear lie groups lie groups which faithfully represented matrix groups method relies proving certain finite dimensional lie subalgebras algebras continuous inversion commute modulo jacobson radical