Displaying similar documents to “The Theory of Transformation Groups / Sophus Lie and Friedrich Engel (Review).”

Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, Karl-Hermann Neeb (2008)

Studia Mathematica

Similarity:

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...

Besov algebras on Lie groups of polynomial growth

Isabelle Gallagher, Yannick Sire (2012)

Studia Mathematica

Similarity:

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

Similarity:

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 As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.