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The strong Morita equivalence for coactions of a finite-dimensional $C^*$-Hopf algebra on unital $C^*$-algebras

Volume 228 / 2015

Kazunori Kodaka, Tamotsu Teruya Studia Mathematica 228 (2015), 259-294 MSC: Primary 46L05; Secondary 46L08. DOI: 10.4064/sm228-3-4

Abstract

Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional $C^*$-Hopf algebra on a Hilbert $C^*$-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional $C^*$-Hopf algebra on unital $C^*$-algebras.

Authors

  • Kazunori KodakaDepartment of Mathematical Sciences
    Faculty of Science
    Ryukyu University
    Nishihara-cho, Okinawa, 903-0213, Japan
    e-mail
  • Tamotsu TeruyaFaculty of Education
    Gunma University
    4-2 Aramaki-machi
    Maebashi City, Gunma, 371-8510, Japan
    e-mail

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