The range of traces on quantum Heisenberg manifolds

Abadie, Beatriz

doi:10.1090/S0002-9947-00-02690-8

The range of traces on quantum Heisenberg manifolds
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Trans. Amer. Math. Soc. 352 (2000), 5767-5780 Request permission

Abstract:

We embed the quantum Heisenberg manifold $D_{\mu \nu }^{c}$ in a crossed product $\mathrm {C}^*$-algebra. This enables us to show that all tracial states on $D_{\mu \nu }^{c}$ induce the same homomorphism on $K_0(D_{\mu \nu }^{c})$, whose range is the group $\mathbf {Z} +2\mu \mathbf {Z} + 2\nu \mathbf {Z}$.

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