Tracing projective modules over noncommutative orbifolds

2021/02/15 by Chakraborty, Sayan · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2102.07691

Abstract

For an action of a finite cyclic group F on an n-dimensional noncommutative torus A_θ, we give sufficient conditions when the fundamental projective modules over A_θ, which determine the range of the canonical trace on A_θ, extend to projective modules over the crossed product C*-algebra A_θ\rtimes F. Our results allow us to understand the range of the canonical trace on A_θ\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 ℤ₂ on any n-dimensional noncommutative torus. As an application, for the flip action of ℤ₂ on a simple n-dimensional torus A_θ, we determine the Morita equivalence class of A_θ\rtimes ℤ₂, in terms of the Morita equivalence class of A_θ.

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