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FROM C*-ALGEBRA EXTENSIONS TO COMPACT QUANTUM METRIC SPACES, QUANTUM SU(2), PODLEŚ SPHERES AND OTHER EXAMPLES

  • PARTHA SARATHI CHAKRABORTY (a1)

Abstract

We construct compact quantum metric spaces starting from a C*-algebra extension with a positive splitting. As special cases, we discuss Toeplitz algebras, quantum SU(2) and Podleś spheres.

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References

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[1]Chakraborty, P. S., ‘Metrics on the quantum Heisenberg manifolds’, J. Operator Theory 54 (2005), 93100.
[2]Connes, A., ‘Compact metric spaces, Fredholm modules, and hyperfiniteness’, Ergod. Th. & Dynam. Sys. 9 (1989), 207220.
[3]Connes, A., Noncommutative Geometry (Academic Press, New York, 1994).
[4]Higson, N. and Roe, J., Analytic K-Homology, Oxford Mathematical Monographs (Oxford University Press, Oxford, 2000).
[5]Li, H., ‘Compact quantum metric spaces and ergodic actions of compact quantum groups’, J. Funct. Anal. 256 (2009), 33683408.
[6]Podleś, P., ‘Quantum spheres’, Lett. Math. Phys. 14 (1987), 193202.
[7]Rieffel, M. A., ‘Metrics on states from actions of compact groups’, Doc. Math. 3 (1998), 215229 (electronic).
[8]Rieffel, M. A., ‘Metrics on state spaces’, Doc. Math. 4 (1999), 559600 (electronic).
[9]Rieffel, M. A., ‘Group C*-algebras as compact quantum metric spaces’, Doc. Math. 7 (2002), 605651 (electronic).
[10]Rieffel, M. A., ‘Gromov–Hausdorff distance for quantum metric spaces. Matrix algebras converge to the sphere for quantum Gromov–Hausdorff distance’, Mem. Amer. Math. Soc. 168 (2004), 796.
[11]Sheu, A. J.-L., ‘Quantization of the Poisson SU(2) and its Poisson homogeneous space—the 2-sphere’, Comm. Math. Phys. 135 (1991), 217232; with an appendix by Jiang-Hua Lu and Alan Weinstein.
[12]Woronowicz, S. L., ‘Twisted SU(2) group. An example of a noncommutative differential calculus’, Publ. RIMS, Kyoto University Univ. 23 (1987), 117181.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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