Model theory and Rokhlin dimension for compact quantum group actions

DOI10.4171/JNCG/337MaRDI QIDQ2327776

Mehrdad Kalantar, Eusebio Gardella, Martino Lupini

Publication date: 15 October 2019

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.10999

zbMATH Keywords

C*-algebracompact quantum groupaxiomatizable classrokhlin propertyquantum group actionlogic for metric structurespositive existential embeddingrokhlin dimension

Mathematics Subject Classification ID

Descriptive set theory (03E15) Noncommutative dynamical systems (46L55) Quantum groups (quantized function algebras) and their representations (20G42) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items

Strongly outer actions of amenable groups on \(\mathcal{Z}\)-stable nuclear \(C^\ast\)-algebras ⋮ The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action ⋮ Traces on ultrapowers of \(\mathrm{C}^{*}\)-algebras ⋮ Rokhlin dimension: duality, tracial properties, and crossed products ⋮ AN INVITATION TO MODEL THEORY AND C*-ALGEBRAS ⋮ Group amenability and actions on \(\mathcal{Z} \)-stable C*-algebras ⋮ Rokhlin dimension of ℤm-actions on simple C∗-algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The pseudoarc is a co-existentially closed continuum
• Uniform spaces and measures
• Model theory of operator algebras. II: Model theory
• Saturation and elementary equivalence of \(C^\ast\)-algebras
• The spatial Rokhlin property for actions of compact quantum groups
• Relative commutants of strongly self-absorbing \(\mathrm{C}^\ast\)-algebras
• Rokhlin dimension for flows
• Crossed products by compact group actions with the Rokhlin property
• Finite group actions on \(C^*\)-algebras with the Rohlin property. I
• Equivariant Poincaré duality for quantum group actions
• The nuclear dimension of \(C^{*}\)-algebras
• A new characterisation of principal actions
• Applications of model theory to \(C^*\)-dynamics
• Crossed products of nuclear \(\mathrm C^{\ast}\)-algebras and their traces
• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum \(SU(2)\) and \(SO(3)\) groups
• Discrete quantum groups
• Rokhlin dimension and \(C^\ast\)-dynamics
• On Kirchberg's embedding problem
• Omitting types and AF algebras
• An invitation to quantum groups and duality. From Hopf algebras to multiplicative unitaries and beyond
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• The operator algebra approach to quantum groups
• Sequentially split ∗-homomorphisms between C*-algebras
• REDUCED PRODUCTS OF METRIC STRUCTURES: A METRIC FEFERMAN–VAUGHT THEOREM
• Actions of compact quantum groups
• FRAÏSSÉ LIMITS OF C*-ALGEBRAS
• Model theory of 𝐶*-algebras
• Finite group actions on certain stably projectionless C*-algebras with the Rohlin property
• The Rohlin property for coactions of finite dimensional $C^*$-Hopf algebras on unital $C^*$-algebras
• Completely positive maps of order zero
• Ultraproducts in Banach space theory.
• Locally compact quantum groups in the von Neumann algebraic setting
• THE JIANG–SU ALGEBRA AS A FRAÏSSÉ LIMIT
• Regularity properties and Rokhlin dimension for compact group actions
• COVERING DIMENSION AND QUASIDIAGONALITY
• The Rohlin property for automorphisms of UHF algebras
• The Haar Measure on a Compact Quantum Group
• Countable saturation of corona algebras
• Rokhlin dimension: duality, tracial properties, and crossed products
• ON THE AXIOMATIZABILITY OF C*-ALGEBRAS AS OPERATOR SYSTEMS
• Rokhlin dimension for compact group actions
• Model theory of operator algebras I: stability
• Model theory of operator algebras III: elementary equivalence and II₁factors
• Locally compact quantum groups