Cartan subalgebras in C*-algebras. Existence and uniqueness

DOI10.1090/tran/7654zbMath1433.46035arXiv1703.10505OpenAlexW2625670074MaRDI QIDQ4967313

Xin Li, Jean N. Renault

Publication date: 3 July 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.10505

zbMATH Keywords

Cartan subalgebrasgroup \(C^{*}\)-algebrashomogeneous \(C^{*}\)-algebras

Mathematics Subject Classification ID

Noncommutative topology (46L85) General theory of (C^*)-algebras (46L05) Topological groupoids (including differentiable and Lie groupoids) (22A22)

Related Items (16)

AF 𝐶*-algebras from non-AF groupoids ⋮ Cartan subalgebras for non-principal twisted groupoid \(C^\ast\)-algebras ⋮ Quasi-locality for étale groupoids ⋮ Constructing C*-diagonals in AH-algebras ⋮ Dynamic asymptotic dimension and Matui's HK conjecture ⋮ The extension of cochain complexes of meromorphic functions to multiplications ⋮ Strict comparison for \(C^*\)-algebras arising from almost finite groupoids ⋮ \(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ Cartan subalgebras and the UCT problem. II ⋮ Noncommutative Cartan \(\mathrm {C}^*\)-subalgebras ⋮ Cartan subalgebras in uniform Roe algebras ⋮ The homology of the Katsura-Exel-Pardo groupoid ⋮ Ideal structure and pure infiniteness of ample groupoid -algebras ⋮ Every classifiable simple C\(^*\)-algebra has a Cartan subalgebra ⋮ CARTAN SUBALGEBRAS IN DIMENSION DROP ALGEBRAS ⋮ A generalization of Renault’s theorem for Cartan subalgebras

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
• Purely infinite simple \(C^\ast\)-algebras that are principal groupoid \(C^\ast\)-algebras
• Decomposition rank of UHF-absorbing \(C^\ast\)-algebras
• Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
• Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups.
• Nuclear dimension and \(\mathcal{Z}\)-stability of pure \(C^{\ast}\)-algebras
• \(C^*\)-simplicity and the unique trace property for discrete groups
• Strict comparison and \(\mathcal{Z}\)-absorption of nuclear \(C^*\)-algebras
• Unique Cartan decomposition for \(\mathrm{II}_1\) factors
• The structure of algebras of operator fields
• The Dirac operator and the principal series for complex semisimple Lie groups
• Nuclear dimension and \(\mathcal Z\)-stability
• On a class of II\(_1\) factors with at most one Cartan subalgebra
• On localizations and simple \(C^*\)-algebras
• A groupoid approach to C*-algebras
• Dynamic characterizations of quasi-isometry and applications to cohomology
• Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra
• Some classifiable groupoid \(C^{*}\)-algebras with prescribed \(K\)-theory
• Crossed products of the Cantor set by free minimal actions of \(\mathbb Z^d\)
• Solid von Neumann algebras.
• The analogues of entropy and of Fisher's information measure in free probability theory. III: The absence of Cartan subalgebras
• Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture
• Cartan subalgebras and the UCT problem
• Unique Cartan decomposition for \(\mathrm{II}_1\) factors arising from arbitrary actions of free groups
• On rigidity of Roe algebras
• Examples of different minimal diffeomorphisms giving the same \(C^*\)-algebras
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Symmetries of the CAR algebra
• Decomposition rank and \(\mathcal{Z}\)-stability
• A survey of Measured Group Theory
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph 𝐶*-algebras and Leavitt path algebras
• Orbit Equivalence and Measured Group Theory
• Homology and topological full groups of étale groupoids on totally disconnected spaces
• The Cancellation Theorem for Projective Modules Over Irrational Rotation C*-Algebras
• K-THEORY FOR THE REDUCED C-ALGEBRA OF A SEMI-SIMPLE LIE GROUP WITH REAL RANK 1 AND FINITE CENTRE
• Generalized Bunce–Deddens algebras
• On a class of II<sub xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> factors with at most one Cartan subalgebra, II
• Cartan subalgebras in C*-algebras
• On C*-Diagonals
• Continuous Trace Groupoid $C^*$-Algebras, II.
• The Regular Group C ∗ -Algebra for Real-Rank One Groups
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. II
• Partial Transformation Groupoids Attached to Graphs and Semigroups
• 1-Bounded entropy and regularity problems in von Neumann algebras
• Continuous orbit equivalence rigidity
• On the structural theory of $\rm II_1$ factors of negatively curved groups
• Strong Solidity of free Araki-Woods factors
• Cantor systems and quasi-isometry of groups
• Non-cyclotomic presentations of modules and prime-order automorphisms of Kirchberg algebras

This page was built for publication: Cartan subalgebras in C*-algebras. Existence and uniqueness