Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
Carri´ on, J
13 Pith papers cite this work. Polarity classification is still indexing.
13
Pith papers citing it
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Introduces discretisation showing independent ample groupoids are equivalent to discrete ones and provides a method to build independent resolutions for computing homology and K-theory.
Introduces tracially reflexive C*-algebras, proves the property for all commutative C*-algebras and all separable dimension-zero ones, and shows it is preserved under inductive limits via Cuntz semigroup and weak Schröder-Simpson criteria.
Stabilized Cuntz–Pimsner algebras decompose as crossed products, yielding new classifications of simplicity, ideals, traces, KMS weights, and quasi-free crossed products.
Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.
Introduces coloured noncommutative entropies and proves variational principles plus generic infinite entropy for endomorphisms of certain classifiable C*-algebras.
Introduces a secondary pairing between subgroups of K-homology and K-theory valued in Q/Z that detects classes missed by the primary pairing and relates it to relative eta invariants, the Thomsen exact sequence, and zeta maps.
New bases, rotation maps, and a metric on the Hausdorffized algebraic K1-group distinguish C*-algebras and *-homomorphisms that agree on the Elliott invariant, the Cuntz semigroup, and its unitary version.
Develops inductive limits and approximate unitary equivalence for C*-tensor category actions on C*-algebras and generalizes Elliott intertwining to classify them up to cocycle conjugacy.
Every stable UCT Kirchberg algebra has a principal étale groupoid model.
Factorial tracially complete C*-algebras with CPoU have real rank zero and stable rank one, giving a description of the Cuntz semigroup including for Z-stable cases.
Establishes Ulam stability for several classes of nuclear C*-algebras with von Neumann targets and derives rigidity results for corona algebras.
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.
citing papers explorer
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Full Gabor frames, its existence problem, and a non-uniform Balian-Low type theorem
Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
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Discretisation and independent resolutions of ample groupoids
Introduces discretisation showing independent ample groupoids are equivalent to discrete ones and provides a method to build independent resolutions for computing homology and K-theory.
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Tracially reflexive C*-algebras
Introduces tracially reflexive C*-algebras, proves the property for all commutative C*-algebras and all separable dimension-zero ones, and shows it is preserved under inductive limits via Cuntz semigroup and weak Schröder-Simpson criteria.
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Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
Stabilized Cuntz–Pimsner algebras decompose as crossed products, yielding new classifications of simplicity, ideals, traces, KMS weights, and quasi-free crossed products.
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Uniqueness for embeddings of nuclear $C^*$-algebras into type II$_{1}$ factors
Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.
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Brown-Voiculescu entropy revisited
Introduces coloured noncommutative entropies and proves variational principles plus generic infinite entropy for endomorphisms of certain classifiable C*-algebras.
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A secondary pairing between K-theory and K-homology, relative eta invariants, and zeta maps
Introduces a secondary pairing between subgroups of K-homology and K-theory valued in Q/Z that detects classes missed by the primary pairing and relates it to relative eta invariants, the Thomsen exact sequence, and zeta maps.
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On the Nielsen-Thomsen sequence
New bases, rotation maps, and a metric on the Hausdorffized algebraic K1-group distinguish C*-algebras and *-homomorphisms that agree on the Elliott invariant, the Cuntz semigroup, and its unitary version.
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An Elliott intertwining approach to classifying actions of C$^*$-tensor categories
Develops inductive limits and approximate unitary equivalence for C*-tensor category actions on C*-algebras and generalizes Elliott intertwining to classify them up to cocycle conjugacy.
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Principal groupoid models for stable UCT Kirchberg algebras
Every stable UCT Kirchberg algebra has a principal étale groupoid model.
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The real and stable rank of tracially complete C*-algebras
Factorial tracially complete C*-algebras with CPoU have real rank zero and stable rank one, giving a description of the Cuntz semigroup including for Z-stable cases.
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Ulam stability for classes of nuclear C*-algebras
Establishes Ulam stability for several classes of nuclear C*-algebras with von Neumann targets and derives rigidity results for corona algebras.
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Nuclear C*-algebras: 99 problems
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.