scholarly journals Relative Morita equivalence of Cuntz–Krieger algebras and flow equivalence of topological Markov shifts

2018 ◽  
Vol 370 (10) ◽  
pp. 7011-7050 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Morita Equivalence ◽  
Markov Shifts ◽  
Flow Equivalence

On C*-Algebras Associated with Subshifts

1997 ◽  
Vol 08 (03) ◽  
pp. 357-374 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Symbolic Dynamics ◽  
Markov Shift ◽  
C Algebra ◽  
C Algebras ◽  
Markov Shifts ◽  
Universal Properties

We construct and study C*-algebras associated with subshifts in symbolic dynamics as a generalization of Cuntz–Krieger algebras for topological Markov shifts. We prove some universal properties for the C*-algebras and give a criterion for them to be simple and purely infinite. We also present an example of a C*-algebra coming from a subshift which is not conjugate to a Markov shift.

scholarly journals Properties of the Secondary Hochschild Homology

2018 ◽  
Vol 25 (02) ◽  
pp. 225-242
Author(s):  
Jacob Laubacher
Keyword(s):  
Exact Sequence ◽  
Morita Equivalence ◽  
Hochschild Homology ◽  
Low Dimension

In this paper we study properties of the secondary Hochschild homology of the triple (A, B, ε) with coefficients in M. We establish a type of Morita equivalence between two triples and show that H•((A, B, ε); M) is invariant under this equivalence. We also prove the existence of an exact sequence which connects the usual and the secondary Hochschild homologies in low dimension, allowing one to perform easy computations. The functoriality of H•((A, B, ε); M) is also discussed.

scholarly journals Irreducible complexity of iterated symmetric bimodal maps

2005 ◽  
Vol 2005 (1) ◽  
pp. 69-85 ◽  
Author(s):  
J. P. Lampreia ◽  
R. Severino ◽  
J. Sousa Ramos
Keyword(s):  
Tree Structure ◽  
Unimodal Maps ◽  
Markov Shifts ◽  
Irreducible Complexity ◽  
The Family

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the∗-product induced on the associated Markov shifts.

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