Displaying similar documents to “On universal enveloping algebras in a topological setting”

Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, Karl-Hermann Neeb (2008)

Studia Mathematica

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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...

Varieties of topological groups, Lie groups and SIN-groups

Karl Hofmann, Sidney Morris, Markus Stroppel (1996)

Colloquium Mathematicae

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In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups

Besov algebras on Lie groups of polynomial growth

Isabelle Gallagher, Yannick Sire (2012)

Studia Mathematica

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We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to H-type groups, this algebra property is generalized to paraproduct estimates.

A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś, Sławomir Turek (2011)

Open Mathematics

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We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.