scholarly journals Locally compact groups appearing as ranges of cocycles of ergodic ℤ-actions

1985 ◽  
Vol 5 (1) ◽  
pp. 47-57 ◽  
Author(s):  
V. Ya. Golodets ◽  
S. D. Sinelshchikov
Keyword(s):  
Dynamical Systems ◽  
Lie Groups ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Separable Group ◽  
Ergodic Automorphism ◽  
Slight Generalization ◽  
Orbit Theory ◽  
Canonical Anticommutation Relations

AbstractThe paper contains the proof of the fact that every solvable locally compact separable group is the range of a cocycle of an ergodic automorphism. The proof is based on the theory of representations of canonical anticommutation relations and the orbit theory of dynamical systems. The slight generalization of reasoning shows further that this result holds for amenable Lie groups as well and can be also extended to almost connected amenable locally compact separable groups.

scholarly journals Qualitative uncertainty principle for the Gabor transform on certain locally compact groups

2018 ◽  
Vol 9 (3) ◽  
pp. 205-220
Author(s):  
Jyoti Sharma ◽  
Ajay Kumar
Keyword(s):  
Lie Groups ◽  
Uncertainty Principle ◽  
Discrete Group ◽  
Locally Compact Groups ◽  
Gabor Transform ◽  
Compact Groups ◽  
Nilpotent Lie Groups ◽  
Locally Compact ◽  
Qualitative Uncertainty ◽  
Low Dimensional

Abstract Several classes of locally compact groups have been shown to possess a qualitative uncertainty principle for the Gabor transform. These include Moore groups, the Heisenberg group {\mathbb{H}_{n}} , the group {\mathbb{H}_{n}\times D} (where D is a discrete group) and other low-dimensional nilpotent Lie groups.

scholarly journals Some properties of locally compact groups

1967 ◽  
Vol 7 (4) ◽  
pp. 433-454 ◽  
Author(s):  
Neil W. Rickert
Keyword(s):  
Compact Group ◽  
Lie Groups ◽  
Locally Compact Group ◽  
Factor Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Arcwise Connected ◽  
New Formulation

In this paper a number of questions about locally compact groups are studied. The structure of finite dimensional connected locally compact groups is investigated, and a fairly simple representation of such groups is obtained. Using this it is proved that finite dimensional arcwise connected locally compact groups are Lie groups, and that in general arcwise connected locally compact groups are locally connected. Semi-simple locally compact groups are then investigated, and it is shown that under suitable restrictions these satisfy many of the properties of semi-simple Lie groups. For example, a factor group of a semi-simple locally compact group is semi-simple. A result of Zassenhaus, Auslander and Wang is reformulated, and in this new formulation it is shown to be true under more general conditions. This fact is used in the study of (C)-groups in the sense of K. Iwasawa.

scholarly journals Locally compact groups with every isometric action bounded or proper

2018 ◽  
Vol 12 (02) ◽  
pp. 267-292
Author(s):  
Romain Tessera ◽  
Alain Valette
Keyword(s):  
Lie Groups ◽  
Local Field ◽  
Algebraic Groups ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Isometric Action ◽  
Locally Compact ◽  
Linear Algebraic Groups ◽  
Isometric Actions

A locally compact group [Formula: see text] has property PL if every isometric [Formula: see text]-action either has bounded orbits or is (metrically) proper. For [Formula: see text], say that [Formula: see text] has property BPp if the same alternative holds for the smaller class of affine isometric actions on [Formula: see text]-spaces. We explore properties PL and BPp and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

Local splitting of locally compact groups and pro-Lie groups

2011 ◽  
Vol 14 (6) ◽  
Author(s):  
Karl H. Hofmann ◽  
Sidney A. Morris
Keyword(s):  
Lie Groups ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Splitting Theorem ◽  
Lie Theory ◽  
Locally Compact

AbstractIn the book “The Lie Theory of Connected Pro-Lie Groups” the authors proved the local splitting theorem for connected pro-Lie groups. George A. A. Michael subsequently proved this theorem for almost connected pro-Lie groups. Here his result is proved more directly using the machinery of the aforementioned book.

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.

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