The soft torus and applications to almost commuting matrices

DOI10.2140/pjm.1993.160.207zbMath0781.46048OpenAlexW1988187144MaRDI QIDQ689738

Ruy Exel

Publication date: 17 November 1993

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/ae1f9a35101e93f8f5a201ca10a3abcdf1d3f11d

zbMATH Keywords

\(K\)-theorysoft torus\(K\)-theory invariantequality of certain invariants associated to almost commuting unitary matricesuniversal \(C^*\)-algebrawinding number invariant

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Index theory (19K56)

Related Items (23)

GROUP QUASI-REPRESENTATIONS AND INDEX THEORY ⋮ Perturbations of the rotation \(C^*\)-algebras and of the Heisenberg commutation relation ⋮ Quasi-representations of groups and two-homology ⋮ Stability of rotation relations in -algebras ⋮ Soft non-commutative toral \(C^*\)-algebras ⋮ Almost commuting orthogonal matrices ⋮ Stability of rotation relations of three unitaries with the flip action in \(C^*\)-algebras ⋮ Approximate symmetries of Hamiltonians ⋮ Stability of rotation relation of two unitaries with \(\mathbb{Z}_3, \mathbb{Z}_4\) and \(\mathbb{Z}_6\)-actions in \(C^*\)-algebras ⋮ Higher dimensional Bott classes and the stability of rotation relations ⋮ Asymptotic unitary equivalence and classification of simple amenable \(C^{\ast}\)-algebras ⋮ On \(C^*\)-algebras related to constrained representations of a free group ⋮ Approximate unitary equivalence in simple $C^{*}$-algebras of tracial rank one ⋮ Simple nuclear \(C^{\ast}\)-algebras not equivariantly isomorphic to their opposites ⋮ COMPUTING CONTINGENCIES FOR STABLE RELATIONS ⋮ Stability of rotation relation of two unitaries with the flip action in \(C^\ast \)-algebras ⋮ \(K\)-theory for the crossed products by certain actions of \(\mathbb Z^2\) ⋮ Finite dimensional representations of the soft torus ⋮ Almost commuting matrices, localized Wannier functions, and the quantum Hall effect ⋮ Stability of certain relations of three unitaries in C∗-algebras ⋮ The Ext class of an approximately inner automorphism ⋮ Noncommutative semialgebraic sets and associated lifting problems ⋮ On the Bott index of unitary matrices on a finite torus

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