Isomorphism classes for quantum Heisenberg manifolds

Details Isomorphism classes for quantum Heisenberg manifolds Isomorphism classes for quantum Heisenberg manifolds

1996-11-23

arxiv.org/abs/funct-an/9611002v1

Mathematics

Operator Algebras

LaTeX, 15 pages

Scientific paper

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 $D^c_{\mu ' \nu '}$ are isomorphic if and only if the parameters $(\mu,\nu)$ and $(\mu ',\nu ')$ belong to the same orbit under the usual action of $GL_2(\ZZ)$ on the torus.

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