Every simple higher dimensional noncommutative torus is an AT algebra

Abstract

We prove that every simple higher dimensional noncommutative torus is an AT algebra.

AMSLaTeX; 22 pages. This paper replaces Sections 5 through 7 of the unpublished long preprint arXiv:math.OA/0306410. A number of minor improvements have been made, particularly near the end

References in corpus (1)

• Finite cyclic group actions with the tracial Rokhlin property

Cited by in corpus (21)

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• The tracial Rokhlin property is generic
• Realization of a simple higher dimensional noncommutative torus as a transformation group C*-algebra
• Topological T-Duality for Twisted Tori
• Gap-labelling conjecture with nonzero magnetic field
• The tracial Rokhlin property for actions of finite groups on C*-algebras
• Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property
• AF-embeddability for Lie groups with $T_1$ primitive ideal spaces
• K-theoretic rigidity and slow dimension growth
• Classification of C*-algebras generated by representations of the unitriangular group $UT(4,\mathbb{Z})$
• Higher dimensional Bott classes and the stability of rotation relations
• Equilibrium on Toeplitz extensions of higher dimensional noncommutative tori
• Metaplectic transformations and finite group actions on noncommutative tori
• Continuous orbit equivalence for automorphismhi systems of equivalence relations
• Compact Lie group actions with continuous Rokhlin property
• Stability of rotation relations in $C^{\ast }$-algebras
• Nonsimplicity of certain universal ${\mathrm{C}}^{\ast }$-algebras
• Lie Bi-Algebras on the Non-Commutative Torus
• Isomorphism and Morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of $S{L}_2(\mathbb{Z})$
• Inverse-Closed Subalgebras of Noncommutative Tori
• Certain actions of finitely generated groups on higher dimensional noncommutative tori