Invariant subsets under compact quantum group actions

Preprint English OPEN
Huang, Huichi;
  • Subject: Mathematics - Operator Algebras | 46L65 (Primary), 16W22 (Secondary) | Mathematics - Quantum Algebra
    arxiv: Mathematics::General Topology

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinit... View more
  • References (24)
    24 references, page 1 of 3

    [1] T. Banica. Fusion rules for representations of compact quantum groups. Exposition. Math. 17 (1999), no. 4, 313-337.

    [2] T. Banica. Representations of compact quantum groups and subfactors. J. Reine Angew. Math. 509 (1999), 167-198.

    [3] E. B´edos, G. J. Murphy, and L. Tuset. Co-amenability of compact quantum groups. J. Geom. Phys. 40 (2001), no. 2, 130-153.

    [4] F. P. Boca. Ergodic actions of compact matrix pseudogroups on C*-algebras. Recent advances in operator algebras, Orl`eans, 1992, Ast´erisque 232 (1995), 93-109.

    [5] J. Cuntz. Simple C∗-algebras generated by isometries. Comm. Math. Phys. 57 (1977), no. 2, 173-185.

    [6] D. Goswami. Quantum symmetries and quantum isometries of compact metric spaces. arXiv: 0811.0095.

    [7] R. Høegh-Krohn, M.B. Landstad and E. Størmer. Compact ergodic groups of automorphisms. Ann. of Math. 114 (1981), no.1, 75-86.

    [8] T. Jech. Set Theory. The third millennium edition, revised and expanded. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003.

    [9] R. Kadison and J. Ringrose. Fundamentals of the Theory of Operator Algebras. Vol. I. Elementary theory. Reprint of the 1983 original. Graduate Studies in Mathematics, 15. American Mathematical Society, Providence, RI, 1997.

    [10] B. Li. Introduction to Operator Algebras. World Scientific Publishing Co., Inc., River Edge, NJ, 1992.

  • Metrics
Share - Bookmark