Isomorphism classes for quantum Heisenberg manifolds

Beatriz Abadie

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arXiv · funct-an/9611002

Isomorphism classes for quantum Heisenberg manifolds

Beatriz Abadie

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Abstract

We embed the quantum Heisenberg manifold in a crossed product algebra. This enables us to show that, in the irrational case, all tracial states on $\dc$ induce the same homomorphism on the K_0-group. We conclude that two irrational quantum Heisenberg manifolds $\dc$ and $D^c_{μ' ν'}$ are isomorphic if and only if the parameters $(μ,ν)$ and $(μ',ν')$ belong to the same orbit under the usual action of $GL_2(\ZZ)$ on the torus.

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Beatriz Abadie. 2020-12-03. Isomorphism classes for quantum Heisenberg manifolds. https://arxiv.org/abs/funct-an/9611002

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