Entropy of automorphisms of \(\text{II}_1\)-factors arising from the dynamical systems theory

DOI10.1006/jfan.2000.3705zbMath0992.46052arXivmath/0002082OpenAlexW2593004250MaRDI QIDQ5937640

Valentin Ya. Golodets, Sergey V. Neshveyev

Publication date: 4 September 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0002082

zbMATH Keywords

Kolmogorov-Sinai entropy\(\text{II}_1\)-factor\(\text{II}_1\)-factor of dynamical systemConnes-Stoermer entropycrossed product

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Entropy and other invariants (28D20) Classifications of (C^*)-algebras (46L35) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items

Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory ⋮ On automorphisms of C*-algebras whose Voiculescu entropy is genuinely non-commutative ⋮ Entropy of automorphisms arising from dynamical systems through discrete groups with amen\-able actions ⋮ Entropy for 𝐶*-algebras with tracial rank zero ⋮ Ergodic theory and maximal abelian subalgebras of the hyperfinite factor

Cites Work

• Unnamed Item
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• Dynamical entropy of C *-algebras and von Neumann algebras
• Entropy of Bogoliubov automorphisms of the canonical anticommutation relations
• Mahler measure and entropy for commuting automorphisms of compact groups
• Une nouvelle définition de l'entropie dynamique des systèmes non commutatifs. (A new definition of dynamical entropy of non-commutative systems)
• Entropy for automorphisms of \(II_1\) von Neumann algebras
• Generators and comparison of entropies of automorphisms of finite von Neumann algebras
• Non-Bernoullian quantum \(K\)-systems
• Topological entropy in exact \(C^*\)-algebras
• Defining quantum dynamical entropy
• Quantum \(K\)-systems
• Index of subfactors and statistics of quantum fields. I
• Dynamical approximation entropies and topological entropy in operator algebras
• Entropy of endomorphisms and relative entropy in finite von Neumann algebras
• Automorphisms of solenoids and p-adic entropy
• Entropy and index for subfactors
• Entropy for Canonical Shifts
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• Entropy of $C^\ast$-dynamical systems defined by bitstreams
• Dynamical entropy for Bogoliubov actions of free abelian groups on the CAR-algebra
• The entropy of rational Powers shifts
• ENTROPY OF BOGOLIUBOV AUTOMORPHISMS OF CAR AND CCR ALGEBRAS WITH RESPECT TO QUASI-FREE STATES
• Dynamical entropy for Bogoliubov actions of torsion-free abelian groups on the CAR-algebra
• ENTROPY FOR CANONICAL SHIFTS AND STRONG AMENABILITY
• Dynamical systems of algebraic origin