TOPOLOGICAL ENTROPY AND AF SUBALGEBRAS OF Graph C*-algebras
نویسنده
چکیده
Abstract. Let AE be the canonical AF subalgebra of a graph C ∗-algebra C∗(E) associated with a locally finite directed graph E. For Brown-Voiculescu’s topological entropy ht(ΦE) of the canonical completely positive map ΦE on C∗(E), ht(ΦE) = ht(ΦE |AE ) = hl(E) = hb(E) is known to hold for a finite graph E, where hl(E) is the loop entropy of Gurevic and hb(E) is the block entropy of Salama. For an irreducible infinite graph E, the inequality hl(E) ≤ ht(ΦE |AE ) has been known recently. It is shown in this paper that ht(ΦE |AE ) ≤ max{hb(E), hb( E)}, where E is the graph E with the direction of the edges reversed. Some Irreducible infinite graphs Ep(p > 1) with ht(ΦE |AEp ) = log p are also examined.
منابع مشابه
C∗-algebras and topological dynamics: finite approximation and paradoxicality
Contents Chapter 1. Introduction 5 Chapter 2. Internal measure-theoretic phenomena 13 1. Amenable groups and nuclearity 13 2. Amenable actions, nuclearity, and exactness 16 3. The type semigroup, invariant measures, and pure infiniteness 21 4. The universal minimal system 29 5. Minimal actions, pure infiniteness, and nuclearity 31 Chapter 3. External measure-theoretic phenomena 33 1. Sofic grou...
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