scholarly journals On the spectrum of operator families on discrete groups over minimal dynamical systems

2017 ◽  
Vol 287 (3-4) ◽  
pp. 993-1007 ◽  
Author(s):  
Siegfried Beckus ◽  
Daniel Lenz ◽  
Marko Lindner ◽  
Christian Seifert
Keyword(s):  
Dynamical Systems ◽  
Discrete Groups ◽  
Minimal Dynamical Systems

scholarly journals Multiplicative combinatorial properties of return time sets in minimal dynamical systems

2019 ◽  
Vol 39 (10) ◽  
pp. 5891-5921
Author(s):  
Daniel Glasscock ◽  
◽  
Andreas Koutsogiannis ◽  
Florian Karl Richter ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Return Time ◽  
Combinatorial Properties ◽  
Minimal Dynamical Systems

scholarly journals Embedding minimal dynamical systems into Hilbert cubes

2020 ◽  
Vol 221 (1) ◽  
pp. 113-166 ◽  
Author(s):  
Yonatan Gutman ◽  
Masaki Tsukamoto
Keyword(s):  
Dynamical Systems ◽  
Minimal Dynamical Systems

scholarly journals UHF-slicing and classification of nuclear C*-algebras

2014 ◽  
Vol 06 (04) ◽  
pp. 465-540 ◽  
Author(s):  
Karen R. Strung ◽  
Wilhelm Winter
Keyword(s):  
Dynamical Systems ◽  
Classification Theorem ◽  
Discrete Version ◽  
C Algebras ◽  
Minimal Dynamical Systems ◽  
Tracial States

In this paper we show that certain simple locally recursive subhomogeneous (RSH) C*-algebras are tracially approximately interval algebras after tensoring with the universal UHF algebra. This involves a linear algebraic encoding of the structure of the local RSH algebra allowing us to find a path through the algebra which looks like a discrete version of [0, 1] and exhausts most of the algebra. We produce an actual copy of the interval and use properties of C*-algebras tensored with UHF algebras to move the honest interval underneath the discrete version. It follows from our main result that such C*-algebras are classifiable by Elliott invariants. Our theorem requires finitely many tracial states that all induce the same state on the K0-group; in particular we do not require that projections separate tracial states. We apply our results to classify some examples of C*-algebras constructed by Elliott to exhaust the invariant. We also give an alternative way to classify examples of Lin and Matui of C*-algebras of minimal dynamical systems. In this way our result can be viewed as a first step towards removing the requirement that projections separate tracial states in the classification theorem for C*-algebras of minimal dynamical systems given by Toms and the second named author.

scholarly journals Skew products and minimal dynamical systems on separable Hilbert manifolds

1984 ◽  
Vol 4 (2) ◽  
pp. 213-224 ◽  
Author(s):  
A. Fathi
Keyword(s):  
Hilbert Space ◽  
Dynamical Systems ◽  
Separable Hilbert Space ◽  
Countable Group ◽  
Locally Compact ◽  
Connected Manifold ◽  
Skew Products ◽  
Minimal Dynamical Systems

AbstractWe prove that any locally compact, non-compact, second countable group acts minimally on any metrizable connected manifold modelled on the separable Hilbert space.

On graph products of multipliers and the Haagerup property for -dynamical systems

2019 ◽  
Vol 40 (12) ◽  
pp. 3188-3216
Author(s):  
SCOTT ATKINSON
Keyword(s):  
Dynamical Systems ◽  
Positive Definite ◽  
Alternative Proof ◽  
Discrete Groups ◽  
Graph Products ◽  
Graph Product ◽  
Haagerup Property ◽  
Products Of Groups ◽  
Product Action

We consider the notion of the graph product of actions of discrete groups $\{G_{v}\}$ on a $C^{\ast }$-algebra ${\mathcal{A}}$ and show that under suitable commutativity conditions the graph product action $\star _{\unicode[STIX]{x1D6E4}}\unicode[STIX]{x1D6FC}_{v}:\star _{\unicode[STIX]{x1D6E4}}G_{v}\curvearrowright {\mathcal{A}}$ has the Haagerup property if each action $\unicode[STIX]{x1D6FC}_{v}:G_{v}\curvearrowright {\mathcal{A}}$ possesses the Haagerup property. This generalizes the known results on graph products of groups with the Haagerup property. To accomplish this, we introduce the graph product of multipliers associated to the actions and show that the graph product of positive-definite multipliers is positive definite. These results have impacts on left-transformation groupoids and give an alternative proof of a known result for coarse embeddability. We also record a cohomological characterization of the Haagerup property for group actions.

scholarly journals Minimal Dynamical Systems on Connected Odd Dimensional Spaces

2015 ◽  
Vol 67 (4) ◽  
pp. 870-892 ◽  
Author(s):  
Huaxin Lin
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Finite Abelian Group ◽  
Finite Covering ◽  
Compact Metric Space ◽  
Covering Dimension ◽  
Group I ◽  
Tracial Rank ◽  
Minimal Dynamical Systems ◽  
Minimal Homeomorphisms

AbstractLet be a minimal homeomorphism (n ≥1). We show that the crossed product has rational tracial rank at most one. Let Ω be a connected, compact, metric space with finite covering dimension and with . Suppose that ,where Gi is a finite abelian group, i = 0,1. Let β:Ω→Ωbe a minimal homeomorphism. We also show that has rational tracial rank at most one and is classifiable. In particular, this applies to the minimal dynamical systems on odd dimensional real projective spaces. This is done by studying minimal homeomorphisms on X✗Ω, where X is the Cantor set.

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