Displaying similar documents to “Dense decompositions of locally compact groups”

Automorphism groups of right-angled buildings: simplicity and local splittings

Pierre-Emmanuel Caprace (2014)

Fundamenta Mathematicae

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We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal. ...

N-determined 2-compact groups. I

Jesper M. Møller (2007)

Fundamenta Mathematicae

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This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know....

Involutions on the second duals of group algebras versus subamenable groups

Ajit Iqbal Singh (2011)

Studia Mathematica

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Let L¹(G)** be the second dual of the group algebra L¹(G) of a locally compact group G. We study the question of involutions on L¹(G)**. A new class of subamenable groups is introduced which is universal for all groups. There is no involution on L¹(G)** for a subamenable group G.

Locally convex algebras which determine a locally compact group

Gholam Hossein Esslamzadeh, Hossein Javanshiri, Rasoul Nasr-Isfahani (2016)

Studia Mathematica

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There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is...