Compact group automorphisms, addition formulas and Fuglede-Kadison determinants

DOI10.4007/annals.2012.176.1.5zbMath1250.22006arXiv1001.0419OpenAlexW2963902483MaRDI QIDQ447931

Hanfeng Li

Publication date: 30 August 2012

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0419

zbMATH Keywords

entropyalgebraic dynamicsFuglede-Kadison determinant

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Topological entropy (37B40)

Related Items (34)

Topological entropy, upper Carath ⋮ A remark on \(\mathbb{T}\)-valued cohomology groups of algebraic group actions ⋮ Fuglede-Kadison determinants and sofic entropy ⋮ Some remarks on the entropy for algebraic actions of amenable groups ⋮ Mean dimension, mean rank, and von Neumann-Lück rank ⋮ A survey of algebraic actions of the discrete Heisenberg group ⋮ The addition theorem for algebraic entropies induced by non-discrete length functions ⋮ The addition theorem for locally monotileable monoid actions ⋮ Combinatorial independence and sofic entropy ⋮ Joint spectrum and the infinite dihedral group ⋮ Algebraic entropy for amenable semigroup actions ⋮ Homoclinically expansive actions and a garden of Eden theorem for harmonic models ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Topological entropy in totally disconnected locally compact groups ⋮ Ore localization of amenable monoid actions and applications toward entropy -- addition formulas and the bridge theorem ⋮ POLISH MODELS AND SOFIC ENTROPY ⋮ ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES ⋮ Sofic mean dimension ⋮ Entropy and the variational principle for actions of sofic groups ⋮ Weak equivalence to Bernoulli shifts for some algebraic actions ⋮ Relative entropy and the Pinsker product formula for sofic groups ⋮ A Juzvinskii addition theorem for finitely generated free group actions ⋮ Homoclinic groups, IE groups, and expansive algebraic actions ⋮ Harmonic models and spanning forests of residually finite groups ⋮ Spectral invariance of \(\ast\)-representations of twisted convolution algebras with applications in Gabor analysis ⋮ Ergodic measures of intermediate entropy for affine transformations of nilmanifolds ⋮ Cost, \(\ell^2\)-Betti numbers and the sofic entropy of some algebraic actions ⋮ Examples in the entropy theory of countable group actions ⋮ Entropy on normed semigroups (towards a unifying approach to entropy) ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Combinatorial independence and naive entropy ⋮ Entropy, determinants, and $L^2$-torsion ⋮ Conditional mean dimension ⋮ Groupoids and Hermitian Banach *-algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symmetry and nonsymmetry for locally compact groups
• Entropy and the variational principle for actions of sofic groups
• Harmonic models and spanning forests of residually finite groups
• Ergodic theory and statistical mechanics
• Relatively spectral morphisms and applications to K-theory
• Entropy range problems and actions of locally normal groups
• Entropy and isomorphism theorems for actions of amenable groups
• Elementary amenable groups
• Mahler measure and entropy for commuting automorphisms of compact groups
• The Abramov-Rokhlin entropy addition formula for amenable group actions
• Mixing automorphisms of compact groups and a theorem of Schlickewei
• The structure of skew products with ergodic group automorphisms
• A class of symmetric and a class of Wiener group algebras
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Proper group actions and the Baum-Connes conjecture
• Weighted group algebras on groups of polynomial growth
• Entropy and mixing for amenable group actions
• Erratum: Math. Ann. 317, 727--750 (2000)
• The Bernoulli property for expansive \(\mathbb Z^ 2\) actions on compact groups
• Über monotone Matrixfunktionen
• Almost block independence and Bernoullicity of \(\mathbb{Z}^ d\)-actions by automorphisms of compact Abelian groups
• Mean topological dimension
• Symmetry and nonsymmetry in the group algebras of discrete groups
• Computing the entropy of a group of endomorphisms
• On the spectral radius of elements in a group algebra
• On the spectrum of convolution operators on groups with polynomial growth
• Determinant theory in finite factors
• $L^2$-determinant class and approximation of $L^2$-Betti numbers
• Fiber entropy and conditional variational principles in compact non-metrizable spaces
• Soficity, amenability, and dynamical entropy
• Sofic entropy and amenable groups
• Entropy for expansive algebraic actions of residually finite groups
• Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents
• An application of Jensen's formula to polynomials
• On Some Inequalities for Polynomials in Several Variables
• The entropy of algebraic actions of countable torsion-free abelian groups
• Measure conjugacy invariants for actions of countable sofic groups
• Orbit-counting for nilpotent group shifts
• Mahler measures and Fuglede--Kadison determinants
• Automorphisms of solenoids and p-adic entropy
• On coincidence of entropies for two classes of dynamical systems
• Homoclinic points of algebraic $\mathbb {Z}^d$-actions
• Division Rings and Group von Neumann Algebras
• Approximating L²‐invariants and the Atiyah conjecture
• p-adic Entropy and a p-adic Fuglede–Kadison Determinant
• Expansive algebraic actions of discrete residually finite amenable groups and their entropy
• Ergodicity and mixing of non-commuting epimorphisms
• Entropy geometry and disjointness for zero-dimensional algebraic actions
• Fuglede–Kadison determinants and entropy for actions of discrete amenable groups
• Subsemigroups of Amenable Groups
• Convolution of invariant measures, maximal entropy
• An amenable group with a nonsymmetric group algebra
• Metric properties of endomorphisms of compact groups
• Entropy for Group Endomorphisms and Homogeneous Spaces
• The Addition Theorem for the Entropy of Transformations of G-Spaces
• Dynamical systems of algebraic origin
• Isomorphism rigidity of irreducible algebraic \(\mathbb{Z}^d\)-actions
• Algebraic actions of the discrete Heisenberg group and other non-abelian groups
• Theory of operator algebras I.
• Entropy theory from the orbital point of view

This page was built for publication: Compact group automorphisms, addition formulas and Fuglede-Kadison determinants