The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
By S. Echterhoff, W. Lück, N. Christopher Phillips, S. Walters. 2006
118 citations recorded by the source corpus.
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 ⋊α F 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 A Θ. Along the way, we prove a number of general results which should have useful applications in other situations.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b054012dcca18e7c24e4de9624469b6f7d0a49ca
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Citations in the corpus
- The tracial Rokhlin property for actions of finite groups on C*-algebras (2006, methodology): “The material of Sections 5 through 7 there will appear in [23], a greatly improved version of Sections 8 through 10 has appeared in [7], and an improved and expanded version of the material in Sections 12 and 13 will appear in [24].”
- On the K-theory of crossed products by automorphic semigroup actions (2012, methodology): “It is taken from [13], but is based on earlier work in [5, 25, 12], and gives a more detailed formulation of the principle (DC) of the introduction:”