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arXiv · 2102.07691

Tracing projective modules over noncommutative orbifolds

Sayan Chakraborty
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Abstract

For an action of a finite cyclic group $F$ on an $n$-dimensional noncommutative torus $A_\theta,$ we give sufficient conditions when the fundamental projective modules over $A_\theta$, which determine the range of the canonical trace on $A_\theta,$ extend to projective modules over the crossed product C*-algebra $A_\theta \rtimes F.$ Our results allow us to understand the range of the canonical trace on $A_\theta \rtimes F$, 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 $\mathbb{Z}_2$ on any $n$-dimensional noncommutative torus. As an application, for the flip action of $\mathbb{Z}_2$ on a simple $n$-dimensional torus $A_\theta$, we determine the Morita equivalence class of $A_\theta \rtimes \mathbb{Z}_2,$ in terms of the Morita equivalence class of $A_\theta.$

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Sayan Chakraborty. 2021-02-15. Tracing projective modules over noncommutative orbifolds. https://arxiv.org/abs/2102.07691

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