scholarly journals C^*-Algebras of algebraic dynamical systems and right LCM semigroups

2018 ◽  
Vol 67 (6) ◽  
pp. 2453-2486 ◽  
Author(s):  
Nathan Brownlowe ◽  
Nadia Larsen ◽  
Nicolai Stammeier
Keyword(s):  
Dynamical Systems ◽  
C Algebras ◽  
Algebraic Dynamical Systems

scholarly journals Surjunctivity and topological rigidity of algebraic dynamical systems

2017 ◽  
Vol 39 (3) ◽  
pp. 604-619 ◽  
Author(s):  
SIDDHARTHA BHATTACHARYA ◽  
TULLIO CECCHERINI-SILBERSTEIN ◽  
MICHEL COORNAERT
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Countable Group ◽  
Continuous Group ◽  
Continuous Map ◽  
Algebraic Dynamical Systems ◽  
Metrizable Group ◽  
Group Automorphisms

Let$X$be a compact metrizable group and let$\unicode[STIX]{x1D6E4}$be a countable group acting on$X$by continuous group automorphisms. We give sufficient conditions under which the dynamical system$(X,\unicode[STIX]{x1D6E4})$is surjunctive, i.e. every injective continuous map$\unicode[STIX]{x1D70F}:X\rightarrow X$commuting with the action of$\unicode[STIX]{x1D6E4}$is surjective.

Sur une notion d'autonomie de systèmes dynamiques, appliquée aux ensembles invariants des flots d' Anosov algébriques

1995 ◽  
Vol 15 (1) ◽  
pp. 175-207 ◽  
Author(s):  
A. Zeghib
Keyword(s):  
Dynamical Systems ◽  
Finite Volume ◽  
Algebraic Dynamical Systems ◽  
Anosov Systems ◽  
Anosov System ◽  
Autonomous Dynamical Systems

AbstractWe introduce a notion of autonomous dynamical systems which generalizes algebraic dynamical systems. We show by giving examples and by describing some properties that this generalization is not a trivial one. We apply the methods then developed to algebraic Anosov systems. We prove that a C1-submanifold of finite volume, which is invariant by an algebraic Anosov system is ‘essentially’ algebraic.

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.

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