scholarly journals Some remarks on the entropy for algebraic actions of amenable groups

2014 ◽  
Vol 367 (12) ◽  
pp. 8579-8595 ◽  
Author(s):  
Nhan-Phu Chung ◽  
Andreas Thom
2018 ◽  
Vol 39 (11) ◽  
pp. 3075-3088 ◽  
Author(s):  
HANFENG LI

We establish a Garden of Eden theorem for expansive algebraic actions of amenable groups with the weak specification property, i.e. for any continuous equivariant map $T$ from the underlying space to itself, $T$ is pre-injective if and only if it is surjective. In particular, this applies to all expansive principal algebraic actions of amenable groups and expansive algebraic actions of $\mathbb{Z}^{d}$ with completely positive entropy.


2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.


2018 ◽  
Vol 25 (3) ◽  
pp. 923-936
Author(s):  
Michael Björklund ◽  
John T. Griesmer
Keyword(s):  

1983 ◽  
Vol 3 (1) ◽  
pp. 129-133 ◽  
Author(s):  
Colin E. Sutherland

AbstractIf K is a countable amenable group acting freely and ergodically on a probability space (Γ, μ), and G is an arbitrary countable amenable group, we construct an injection of the space of unitary representations of G into the space of unitary 1-cocyles for K on (Γ, μ); this injection preserves intertwining operators. We apply this to show that for many of the standard non-type-I amenable groups H, the representation theory of H contains that of every countable amenable group.


2021 ◽  
Vol 1 (7) ◽  
pp. 69-79
Author(s):  
Aleksandr I. Barulin ◽  

Introduction. Vertical steel tanks are extensively used in oil fields to hold crude oil and other liquids. Their construction requires continuous surveying control. However, measurement procedures, data processing, and deviations and documentation correction are not universal and cannot be applied for tanks with a capacity of less than 3000 m3. Moreover, the process of correcting the detected bottom irregularities is poorly substantiated and intuitive. Research objective is to improve the as-built survey accuracy and reliability of the low-capacity steel tank bottom, substantiate the minimum height of its irregularities, increase the objectivity and productivity of measurement processing, develop an unambiguous method for time-predictable correction of bottom irregularities, and substantiate the optimal contents of its relief’s as-built scheme. Methods of research. Geometric leveling for the bottom profile survey failed to provide adequate accuracy and was therefore replaced by the method of trigonometric leveling. A method has been developed for determining the deviations of the existent tank bottom profile from the design position by means of algebraic actions with surfaces of a topographic order. The accuracy of determining the smallest height of bottom irregularities has been estimated under the tacheometric survey. A method has been proposed for controlling the correction of tank bottom irregularities based on evaluation calculations of bottom deformations by the finite element method. Research results. All the development results are exemplified by a specific production example. It was found that for a full completion of work, two iterations of tank bottom irregularities correction are enough. Methods of optimal design for the facility’s as-built schemes are presented. Conclusions. A simple, accurate, low-cost, productive, and time-predictable method of mine surveying, mathematical processing and correction of deviations in the tank bottom profile has been developed. This technique reduces the construction period and increases the operating time of the facility.


2021 ◽  
Vol 65 (4) ◽  
Author(s):  
Amos Nevo ◽  
Felix Pogorzelski
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document