The structure of crossed products of irrational rotation algebras by finite subgroups of SL_2 (Z)

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dc.creatorEchterhoff, Siegfried
dc.creatorLueck, Wolfgang
dc.creatorPhillips, N. Christopher
dc.creatorWalters, Samuel
dc.date2006-09-28
dc.date2006-09-28
dc.date.accessioned2026-07-07T07:25:21Z
dc.date.available2026-07-07T07:25:21Z
dc.descriptionLet F be a finite subgroup of SL_2 (Z) (necessarily isomorphic to one of Z/2Z, Z/3Z, Z/4Z, or Z/6Z), and let F act on the irrational rotational algebra A_θ via the restriction of the canonical action of SL_2 (Z). Then the crossed product of A_θ by F, and the fixed point algebra for the action of F on A_θ, are AF algebras. The same is true for the crossed product and fixed point algebra of the flip action of Z/2Z 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.
dc.descriptionAMSLaTeX; 43 pages. This paper is a greatly improved version of Sections 8 through 10 of the unpublished long preprint arXiv:math.OA/0306410. In particular, the conclusion that the crossed products and fixed point algebras for the actions of Z/3Z, Z/4Z, and Z/6Z on A_θ are AH algebras has been improved to state that they are AF algebras, and the ordered K-theory has been completely determined
dc.identifierhttps://arxiv.org/abs/math/0609784
dc.identifierhttp://arxiv.org/abs/math/0609784
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116687
dc.subjectOperator Algebras
dc.subject19K14, 46L35, 46L55, 46L80 (Primary); 18F25, 19K99, 46L40 (Secondary)
dc.titleThe structure of crossed products of irrational rotation algebras by finite subgroups of SL_2 (Z)
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