A cohomological characterization of amenable actions

1991 ◽  
Vol 110 (3) ◽  
pp. 491-504
Author(s):  
C. Anantharaman-Delaroche
Keyword(s):  
Dynamical Systems ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Classical Characterization

AbstractWe give a new characterization of amenability for dynamical systems, in cohomological terms, which generalizes the classical characterization of amenable locally compact groups stated by Johnson.

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.

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 Amenable dynamical systems over locally compact groups

2021 ◽  
pp. 1-41
Author(s):  
ALEX BEARDEN ◽  
JASON CRANN
Keyword(s):  
Dynamical Systems ◽  
Approximation Property ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Weak Approximation ◽  
Locally Compact ◽  
Completely Positive ◽  
Cambridge Philos ◽  
Schur Multipliers ◽  
Approximation Of The Identity

Abstract We establish several new characterizations of amenable $W^*$ - and $C^*$ -dynamical systems over arbitrary locally compact groups. In the $W^*$ -setting we show that amenability is equivalent to (1) a Reiter property and (2) the existence of a certain net of completely positive Herz–Schur multipliers of $(M,G,\alpha )$ converging point weak* to the identity of $G\bar {\ltimes }M$ . In the $C^*$ -setting, we prove that amenability of $(A,G,\alpha )$ is equivalent to an analogous Herz–Schur multiplier approximation of the identity of the reduced crossed product $G\ltimes A$ , as well as a particular case of the positive weak approximation property of Bédos and Conti [On discrete twisted $C^*$ -dynamical systems, Hilbert $C^*$ -modules and regularity. Münster J. Math.5 (2012), 183–208] (generalized to the locally compact setting). When $Z(A^{**})=Z(A)^{**}$ , it follows that amenability is equivalent to the1-positive approximation property of Exel and Ng [Approximation property of $C^*$ -algebraic bundles. Math. Proc. Cambridge Philos. Soc.132(3) (2002), 509–522]. In particular, when $A=C_0(X)$ is commutative, amenability of $(C_0(X),G,\alpha )$ coincides with topological amenability of the G-space $(G,X)$ .

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.

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