Tracing projective modules over noncommutative orbifolds

Article Type

Research Article

Publication Title

Journal of Noncommutative Geometry

Abstract

For an action of a finite cyclic group F on an n-dimensional noncommutative torus Aθ , we give sufficient conditions when the fundamental projective modules over Aθ , which determine the range of the canonical trace on Aθ , extend to projective modules over the crossed product C*- algebra Aθ Ì F . Our results allow us to understand the range of the canonical trace on Aθ Ì F, and determine it completely for several examples including the crossed products of 2-dimensional noncommutative tori with finite cyclic groups and the flip action of Z2 on any n-dimensional noncommutative torus. As an application, for the flip action of Z2 on a simple n-dimensional torus Aθ , we determine the Morita equivalence class of Aθ Ì Z2, in terms of the Morita equivalence class of Aθ

First Page

385

Last Page

406

DOI

https://10.4171/JNCG/487

Publication Date

1-1-2023

Comments

Open Access, Gold, Green

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