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The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
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Siegfried Echterhoff
Published/Copyright:
January 20, 2010
Abstract
Let F ⊆ SL2(ℤ) be a finite subgroup (necessarily isomorphic to one of ℤ2, ℤ3, ℤ4, or ℤ6), and let F act on the irrational rotational algebra Aθ via the restriction of the canonical action of SL2(ℤ). Then the crossed product Aθ ⋊αF and the fixed point algebra 
are AF algebras. The same is true for the crossed product and fixed point algebra of the flip action of ℤ2 on any simple d-dimensional noncommutative torus AΘ. Along the way, we prove a number of general results which should have useful applications in other situations.
Received: 2008-10-15
Published Online: 2010-01-20
Published in Print: 2010-February
© Walter de Gruyter Berlin · New York 2010
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- Deformation quantization of surjective submersions and principal fibre bundles
- Complete moduli spaces of branchvarieties
- DG-algebras and derived A∞-algebras
- Subshifts and perforation
- On a conjecture of Atkin
- Mukai duality for gerbes with connection
- The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
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Articles in the same Issue
- Deformation quantization of surjective submersions and principal fibre bundles
- Complete moduli spaces of branchvarieties
- DG-algebras and derived A∞-algebras
- Subshifts and perforation
- On a conjecture of Atkin
- Mukai duality for gerbes with connection
- The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
- On a conjecture of Borwein, Bradley and Broadhurst
