Fuglede-Kadison determinants and sofic entropy

DOI10.1007/s00039-016-0370-yzbMath1377.22005arXiv1402.1135OpenAlexW3099861113MaRDI QIDQ2628931

Ben Hayes

Publication date: 19 July 2016

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.1135

zbMATH Keywords

von Neumann algebraspectral measuretopological entropymetric entropyalgebraic actionssofic entropysofic groupFuglede-Kadison determinantsgroup von Neumann algebrasofic approximation

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Group algebras of locally compact groups (22D15)

Related Items (24)

Entropy, products, and bounded orbit equivalence ⋮ A remark on \(\mathbb{T}\)-valued cohomology groups of algebraic group actions ⋮ The entropy of Gibbs measures on sofic groups ⋮ Continuous cocycle superrigidity for coinduced actions and relative ends ⋮ Announce of an entropy formula for a class of actions coming from Gibbs measures ⋮ New examples of Bernoulli algebraic actions ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Free energy, Gibbs measures, and Glauber dynamics for nearest-neighbor interactions ⋮ Sofic entropy of Gaussian actions ⋮ POLISH MODELS AND SOFIC ENTROPY ⋮ Weak equivalence to Bernoulli shifts for some algebraic actions ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy ⋮ Relative entropy and the Pinsker product formula for sofic groups ⋮ Mahler's work and algebraic dynamical systems ⋮ The work of Lewis Bowen on the entropy theory of non-amenable group actions ⋮ Cost, \(\ell^2\)-Betti numbers and the sofic entropy of some algebraic actions ⋮ Entropy, Shannon orbit equivalence, and sparse connectivity ⋮ Positive entropy actions of countable groups factor onto Bernoulli shifts ⋮ Examples in the entropy theory of countable group actions ⋮ Sofic mean length ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups ⋮ Harmonic models and Bernoullicity

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