Group Dynamical Systems on $$C^{*}$$-Algebras Generated by Countable Infinitely Many Semicircular Elements

2021 ◽  
pp. 159-205
Author(s):  
Ilwoo Cho
Keyword(s):  
Dynamical Systems ◽  
C Algebras ◽  
Semicircular Elements

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 C⁎-algebras associated to Boolean dynamical systems

2017 ◽  
Vol 450 (1) ◽  
pp. 727-768 ◽  
Author(s):  
Toke Meier Carlsen ◽  
Eduard Ortega ◽  
Enrique Pardo
Keyword(s):  
Dynamical Systems ◽  
C Algebras

scholarly journals $C^{*}$ -algebras associated with shift dynamical systems

1984 ◽  
Vol 36 (2) ◽  
pp. 279-293
Author(s):  
Shinzo KAWAMURA ◽  
Hideo TAKEMOTO
Keyword(s):  
Dynamical Systems ◽  
C Algebras
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