LOCALLY COMPACT GROUPS ADMITTING FAITHFUL STRONGLY CHAOTIC ACTIONS ON HAUSDORFF SPACES

2013 ◽  
Vol 23 (09) ◽  
pp. 1350158 ◽  
Author(s):  
FRIEDRICH MARTIN SCHNEIDER ◽  
SEBASTIAN KERKHOFF ◽  
MIKE BEHRISCH ◽  
STEFAN SIEGMUND
Keyword(s):  
Hausdorff Space ◽  
Geometric Characterization ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Action

In this paper we provide a geometric characterization of those locally compact Hausdorff topological groups which admit a faithful strongly chaotic continuous action on some Hausdorff space.

scholarly journals A Note on Amenability of Locally Compact Quantum Groups

2014 ◽  
Vol 57 (2) ◽  
pp. 424-430 ◽  
Author(s):  
Piotr M. Sołtan ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Short Note ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups

AbstractIn this short note we introduce a notion called quantum injectivity of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. In particular, this provides a new characterization of amenability of locally compact groups.

A decomposition theorem for locally compact groups

2019 ◽  
Vol 26 (1) ◽  
pp. 29-33
Author(s):  
Sanjib Basu ◽  
Krishnendu Dutta
Keyword(s):  
Compact Group ◽  
Lebesgue Point ◽  
Decomposition Theorem ◽  
Locally Compact Group ◽  
The Other ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Interesting Connection

Abstract We prove that, under certain restrictions, every locally compact group equipped with a nonzero, σ-finite, regular left Haar measure can be decomposed into two small sets, one of which is small in the sense of measure and the other is small in the sense of category, and all such decompositions originate from a generalised notion of a Lebesgue point. Incidentally, such class of topological groups for which this happens turns out to be metrisable. We also observe an interesting connection between Luzin sets in such spaces and decompositions of the above type.

scholarly journals Locally compact products and coproducts in categories of topological groups

1977 ◽  
Vol 17 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Karl Heinrich Hofmann ◽  
Sidney A. Morris
Keyword(s):  
Abelian Groups ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Torsion Free Group ◽  
Locally Compact Abelian Groups ◽  
Discrete Torsion ◽  
Compact Abelian Groups ◽  
Torsion Free

In the category of locally compact groups not all families of groups have a product. Precisely which families do have a product and a description of the product is a corollary of the main theorem proved here. In the category of locally compact abelian groups a family {Gj; j ∈ J} has a product if and only if all but a finite number of the Gj are of the form Kj × Dj, where Kj is a compact group and Dj is a discrete torsion free group. Dualizing identifies the families having coproducts in the category of locally compact abelian groups and so answers a question of Z. Semadeni.

Characterization of non-compact locally compact groups by cocompact subgroups

2020 ◽  
Vol 23 (1) ◽  
pp. 17-24
Author(s):  
Bilel Kadri
Keyword(s):  
Topological Group ◽  
Finite Index ◽  
Quotient Space ◽  
Open Subgroup ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

AbstractA subgroup H of a topological group G is called cocompact (or uniform) if the quotient space {G/\overline{H}} is compact, where {\overline{H}} denotes the closure of H in G. The purpose of this paper is to give a characterization of non-compact locally compact groups with the property that every non-trivial closed (respectively, open) subgroup is cocompact (respectively, has finite index).

scholarly journals LOCALLY COMPACT WREATH PRODUCTS

2018 ◽  
Vol 107 (1) ◽  
pp. 26-52 ◽  
Author(s):  
YVES CORNULIER
Keyword(s):  
Normal Subgroup ◽  
Wreath Product ◽  
Natural Extension ◽  
Wreath Products ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Locally Compact ◽  
Intermediate Growth ◽  
Compactly Generated

Wreath products of nondiscrete locally compact groups are usually not locally compact groups, nor even topological groups. As a substitute introduce a natural extension of the wreath product construction to the setting of locally compact groups. Applying this construction, we disprove a conjecture of Trofimov, constructing compactly generated locally compact groups of intermediate growth without any open compact normal subgroup.

Studies in harmonic analysis

1964 ◽  
Vol 60 (3) ◽  
pp. 465-516 ◽  
Author(s):  
N. Th. Varopoulos
Keyword(s):  
Harmonic Analysis ◽  
Complete Characterization ◽  
Locally Compact Groups ◽  
Topological Spaces ◽  
Compact Groups ◽  
Measure Algebra ◽  
Topological Groups ◽  
Inductive Limits ◽  
Locally Compact ◽  
Character Group

In this paper we shall be mainly concerned with the following three apparently widely differing questions.(a) What are the possible group topologies on an Abelian group that have a given, fixed continuous character group?In developing our theory, we are very strongly motivated by the duality theory of linear topological spaces and in particular by Mackey's theorem of that theory. This important result gives a complete characterization of all locally convex topologies on a linear space that have a given, fixed, separating dual space. The analogue of Mackey's theorem for groups, together with related results, is examined in sections 1 and 2 of part 2 of the paper.(b) What are the properties of topological groups that are denumerable inductive limits of locally compact groups? (See section 1 of part 1 of the paper for definitions.)Our aim here is to extend results known for locally compact groups to this larger class of groups. The topological study of these groups is carried out in section 3 of part 1 of the paper and the really deep results about their characters are proved in section 5 of part 3 of the paper, as applications of the theory developed in that part of the paper, which is a type of harmonic analysis for these groups.(c) What are the properties of certain algebras of measures of a locally compact group G, that strictly contain L1(G), and share most of the pleasing properties of L1(G), that is, they do not have any of the pathological features of the full measure algebra M(G) such as the Wiener–Pitt phenomenon or asymmetry?

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