Finite-dimensional Lie subalgebras of algebras with continuous inversion

• Autorzy: Daniel Beltiţă , Karl-Hermann Neeb
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H30: Functional calculus in topological algebras
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties
• 17B30: Solvable, nilpotent (super)algebras
• 22E15: General properties and structure of real Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 3
• Strony: 249-262

Daty

wydano

2008

Twórcy

autor

Daniel Beltiţă

• Institute of Mathematics "Simion Stoilow", of the Romanian Academy, P.O. Box 1-764, Bucureşti, Romania

autor

Karl-Hermann Neeb

• Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany

Identyfikatory

DOI

10.4064/sm185-3-3