Symmetrized non-commutative tori revisited

2022/04/25 by Chakraborty, Sayan · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2204.11546

Abstract

For the flip action of ℤ₂ on an n-dimensional noncommutative torus A_θ, using an exact sequence by Natsume, we compute the K-theory groups of A_θ\rtimes ℤ₂. The novelty of our method is that it also provides an explicit basis of K₀(A_θ\rtimes ℤ₂), for any θ. As an application, for a simple n-dimensional torus A_θ, using classification techniques, we determine the isomorphism class of A_θ\rtimes ℤ₂ in terms of the isomorphism class of A_θ.

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