Tracing projective modules over noncommutative orbifolds
Sayan Chakraborty
Indian Statistical Institute, Kolkata, India
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Abstract
For an action of a finite cyclic group on an -dimensional noncommutative torus , we give sufficient conditions when the fundamental projective modules over , which determine the range of the canonical trace on , extend to projective modules over the crossed product -algebra . Our results allow us to understand the range of the canonical trace on , 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 on any -dimensional noncommutative torus. As an application, for the flip action of on a simple -dimensional torus , we determine the Morita equivalence class of in terms of the Morita equivalence class of $A_\theta.
Cite this article
Sayan Chakraborty, Tracing projective modules over noncommutative orbifolds. J. Noncommut. Geom. 17 (2023), no. 2, pp. 385–406
DOI 10.4171/JNCG/487