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- W2563661216 abstract "We study the entropy for an automorphism and the Haagerup invariant in a relation to a discrete group which admits an amenable action on a compact space. By picking up the free group F∞ as such a group, first we show that the Brown-Germain entropy of the free shift σ ∈ Aut( F∞) is zero. This implies that for the automorphisms induced by σ on the reduced C-algebra and the von Neumann algebra, the Brown-Voiculescu topological entropy, the Connes-Narnhofer-Thirring dynamical entropy and the Connes-Stormer entropy are all zero. Second, for such a group G, we show the following relation on the Haagerup invariant Λ(·) that Λ((l(G) ⊗ A) ×αG⊗α G) = Λ(l (G) ⊗ A) = Λ(A) for all C-dynamical system (A,G, α), where α is the canonical action." @default.
- W2563661216 created "2017-01-06" @default.
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- W2563661216 date "2006-01-01" @default.
- W2563661216 modified "2023-09-27" @default.
- W2563661216 title "Entropy and the Haagerup Invariant Related to Groups with Amenable Actions" @default.
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