The range of traces on quantum Heisenberg manifolds
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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 $\mathbf {Z} +2\mu \mathbf {Z} + 2\nu \mathbf {Z}$.References
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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
- 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.
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1781278