Entropy of shifts on topological graph C^*-algebras

2009/01/02 by Valentin Deaconu, Deaconu, Valentin
Mathematics · #46L05 #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.0901.0196

arxiv created 2009/01/02 · openalex publication_date 2009/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give entropy estimates for two canonical non commutative shifts on C^*-algebras associated to some topological graphs E=(E⁰,E¹,s,r), defined using a basis of the corresponding Hilbert bimodule H(E). We compare their entropies with the growth entropies associated directly to the topological graph. We illustrate with some examples of topological graphs considered by Katsura, where the vertex and the edge spaces are a union of unit circles and more detailed computations can be done.

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