Finite-dimensional Lie subalgebras of algebras with continuous inversion

Details Finite-dimensional Lie subalgebras of algebras with continuous inversion Finite-dimensional Lie subalgebras of algebras with continuous inversion

2006-03-17

arxiv.org/abs/math/0603420v2

Mathematics

Functional Analysis

9 pages; to appear in the journal Studia Mathematica

Scientific paper

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.

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