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Topological entropy for countable Markov shifts and Exel--Laca algebras

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arxiv 2212.14607 v1 pith:K7EJQAN4 submitted 2022-12-30 math.OA math.DS

Yuta Michimoto , Yushi Nakano , Hisayoshi Toyokawa , Keisuke Yoshida This is my paper · ORCID
classification math.OAmath.DS
keywords entropytopologicalassociatedconditionscountableexel--lacafinitemarkov
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abstract

We show that the (Gurevich) topological entropy for the countable Markov shift associated with an infinite transition matrix $A$ coincides with the non-commutative topological entropy for the Exel--Laca algebra associated with $A$, under certain conditions on $A$. An important example satisfying the conditions is the renewal shift, which is not locally finite. We also pose interesting questions for future research on non-commutative topological entropy for non-locally finite transition matrices.

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Cited by 1 Pith paper

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  1. Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts

    math.DS 2025-06 conditional novelty 6.0 of 10

    Continuous extendability of the shift map to the generalized Markov shift is equivalent to existence of a *-endomorphism of the commutative C*-algebra D_A, yielding explicit spectral radius formulas for weighted endom...

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