scholarly journals State splitting, strong shift equivalence and stable isomorphism of Cuntz–Krieger algebras

2018 ◽  
Vol 34 (1) ◽  
pp. 93-112
Author(s):  
Kengo Matsumoto
Keyword(s):  
Strong Shift ◽  
Shift Equivalence ◽  
State Splitting ◽  
Strong Shift Equivalence

scholarly journals Strong shift equivalence of 2 × 2 matrices of non-negative integers

1983 ◽  
Vol 3 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Kirby A. Baker
Keyword(s):  
Markov Chains ◽  
Sufficient Conditions ◽  
Topological Isomorphism ◽  
Strong Shift ◽  
Shift Equivalence ◽  
Integral Matrices ◽  
Strong Shift Equivalence

AbstractThe concept of strong shift equivalence of square non-negative integral matrices has been used by R. F. Williams to characterize topological isomorphism of the associated topological Markov chains. However, not much has been known about sufficient conditions for strong shift equivalence even for 2×2 matrices (other than those of unit determinant). The main theorem of this paper is: If A and B are positive 2×2 integral matrices of non-negative determinant and are similar over the integers, then A and B are strongly shift equivalent.

Strong shift equivalence and strong Conley index

2015 ◽  
Vol 31 (3) ◽  
pp. 280-292
Author(s):  
Sainkupar Marwein Mawiong ◽  
Himadri Kumar Mukerjee
Keyword(s):  
Conley Index ◽  
Strong Shift ◽  
Shift Equivalence ◽  
Strong Shift Equivalence

scholarly journals Path Methods for Strong Shift Equivalence of Positive Matrices

2013 ◽  
Vol 126 (1) ◽  
pp. 65-115 ◽  
Author(s):  
Mike Boyle ◽  
K. H. Kim ◽  
F. W. Roush
Keyword(s):  
Strong Shift ◽  
Shift Equivalence ◽  
Positive Matrices ◽  
Strong Shift Equivalence

scholarly journals Strong shift equivalence of C*-correspondences

2008 ◽  
Vol 167 (1) ◽  
pp. 315-346 ◽  
Author(s):  
Paul S. Muhly ◽  
David Pask ◽  
Mark Tomforde
Keyword(s):  
Strong Shift ◽  
Shift Equivalence ◽  
Strong Shift Equivalence

scholarly journals On strong shift equivalence over a Boolean semiring

1986 ◽  
Vol 6 (1) ◽  
pp. 81-97 ◽  
Author(s):  
Ki Hang Kim ◽  
Fred W. Roush
Keyword(s):  
Equivalence Relation ◽  
Equivalence Classes ◽  
Directed Edge ◽  
Strong Shift ◽  
Shift Equivalence ◽  
Edge Graph ◽  
Boolean Semiring ◽  
Strong Shift Equivalence

AbstractShift equivalence is the relation between A, B that there exists S, R, n > 0 with RA = BR, AS = SB, SR = An, RS = Bn. Strong shift equivalence is the equivalence relation generated by these equations with n = 1. We prove that for many Boolean matrices strong shift equivalence is characterized by shift equivalence and a trace condition. However, we also show that if A is strongly shift equivalent to B, then there exists a homomorphism from an iterated directed edge graph of A to the graph of B preserving the traces of powers. This yields results on colourings of iterated directed edge graphs and might distinguish new strong equivalence classes.

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