Mean dimension, mean rank, and von Neumann-Lück rank

DOI10.1515/crelle-2015-0046zbMath1392.37018arXiv1307.5471OpenAlexW2963329151MaRDI QIDQ1637088

Hanfeng Li, Bingbing Liang

Publication date: 7 June 2018

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5471

zbMATH Keywords

von Neumann algebratopological entropyBetti numbermean dimension

Mathematics Subject Classification ID

Related Items (19)

Fuglede-Kadison determinants and sofic entropy ⋮ Some remarks on the entropy for algebraic actions of amenable groups ⋮ The addition theorem for algebraic entropies induced by non-discrete length functions ⋮ Mean dimension theory in symbolic dynamics for finitely generated amenable groups ⋮ Variational principles for amenable metric mean dimensions ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Mean dimension of natural extension of algebraic systems ⋮ Sylvester rank functions for amenable normal extensions ⋮ Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Large dynamics of Yang-Mills theory: mean dimension formula ⋮ Double variational principle for mean dimension with potential ⋮ Double variational principle for mean dimension ⋮ Sofic mean length ⋮ Entropy on normed semigroups (towards a unifying approach to entropy) ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Symbolic dynamics in mean dimension theory ⋮ Mean topological dimension for random bundle transformations ⋮ Conditional mean dimension

Cites Work

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• Compact group automorphisms, addition formulas and Fuglede-Kadison determinants
• On Turing dynamical systems and the Atiyah problem
• Minimal systems of arbitrary large mean topological dimension
• Ergodic theory and statistical mechanics
• On the local cross-sections in locally compact groups
• Amenable groups, mean topological dimension and subshifts
• Entropy and isomorphism theorems for actions of amenable groups
• Entropy on discrete Abelian groups
• Elementary amenable groups
• Mahler measure and entropy for commuting automorphisms of compact groups
• Mean dimension, small entropy factors and an embedding theorem
• The spectral measure of certain elements of the complex group ring of a wreath product
• Mean topological dimension
• Topological invariants of dynamical systems and spaces of holomorphic maps. I.
• Homoclinic groups, IE groups, and expansive algebraic actions
• Sofic mean dimension
• Mean topological dimension for actions of discrete amenable groups
• Irrational \(l^2\) invariants arising from the lamplighter group
• On the dimension of homogeneous spaces
• On a question of Atiyah
• Free lamplighter groups and a question of Atiyah
• Entropy, determinants, and $L^2$-torsion
• Rational group ring elements with kernels having irrational dimension
• Embedding ℤ^k-actions in cubical shifts and ℤ^k-symbolic extensions
• Closed manifolds with transcendentalL²-Betti numbers:
• Some remarks on the entropy for algebraic actions of amenable groups
• Cellular Automata and Groups
• Deformation of Brody curves and mean dimension
• Division Rings and Group von Neumann Algebras
• Dimension theory of arbitrary modules over finite von Neumann algebras and L2-Betti numbers I: Foundations
• The rank of finitely generated modules over group algebras
• ON THE ANALYTIC ZERO DIVISOR CONJECTURE OF LINNELL
• Length functions, multiplicities and algebraic entropy
• Moduli Space of Brody Curves, Energy and Mean Dimension
• A GENERALIZATION OF THE CONCEPT OF LENGTH
• Dynamical systems of algebraic origin
• Theory of operator algebras I.
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum

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