Soficity, amenability, and dynamical entropy

Abstract

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical counterparts when the acting group is amenable.

Minor change. To appear in Amer. J. Math

References in corpus (1)

• Entropy and the variational principle for actions of sofic groups

Cited by in corpus (3)

• An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic Groups
• An l^{p}-Version of von Neumann Dimension for Representations of Equivalence Relations
• Branching of Representations to Symmetric Subgroups