Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, and Karl-Hermann Neeb. "Finite-dimensional Lie subalgebras of algebras with continuous inversion." Studia Mathematica 185.3 (2008): 249-262. <http://eudml.org/doc/284410>.

@article{DanielBeltiţă2008,
abstract = {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.},
author = {Daniel Beltiţă, Karl-Hermann Neeb},
journal = {Studia Mathematica},
keywords = {linear Lie group; faithful representation, algebra with continuous inversion},
language = {eng},
number = {3},
pages = {249-262},
title = {Finite-dimensional Lie subalgebras of algebras with continuous inversion},
url = {http://eudml.org/doc/284410},
volume = {185},
year = {2008},
}

TY - JOUR
AU - Daniel Beltiţă
AU - Karl-Hermann Neeb
TI - Finite-dimensional Lie subalgebras of algebras with continuous inversion
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 3
SP - 249
EP - 262
AB - 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.
LA - eng
KW - linear Lie group; faithful representation, algebra with continuous inversion
UR - http://eudml.org/doc/284410
ER -