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The range of traces on quantum Heisenberg manifolds


Author: Beatriz Abadie
Journal: Trans. Amer. Math. Soc. 352 (2000), 5767-5780
MSC (2000): Primary 46L80; Secondary 46L55
DOI: https://doi.org/10.1090/S0002-9947-00-02690-8
Published electronically: August 21, 2000
MathSciNet review: 1781278
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Abstract:

We embed the quantum Heisenberg manifold $D_{\mu\nu}^{c}$ in a crossed product ${C}^*$-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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Additional Information

Beatriz Abadie
Affiliation: Centro de Matemáticas, Facultad de Ciencias, Iguá 4225, CP 11 400, Montevideo, Uruguay
Email: abadie@cmat.edu.uy

DOI: https://doi.org/10.1090/S0002-9947-00-02690-8
Received by editor(s): December 2, 1996
Published electronically: August 21, 2000
Additional Notes: Partially supported by Conicyt (Proyecto 2002), Uruguay. Part of the material in this work was contained in the author’s Ph.D. dissertation submitted to the University of California at Berkeley in May 1992.
Article copyright: © Copyright 2000 American Mathematical Society

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