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The Crossed Product of Finite Hopf C *-Algebra and C *-Algebra

Author

Listed:
  • Xiaomin Wei

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Lining Jiang

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Dianlu Tian

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

Let H be a finite Hopf C * -algebra and A a C * -algebra of finite dimension. In this paper, we focus on the crossed product A ⋊ H arising from the action of H on A , which is a ∗-algebra. In terms of the faithful positive Haar measure on a finite Hopf C * -algebra, one can construct a linear functional on the ∗-algebra A ⋊ H , which is further a faithful positive linear functional. Here, the complete positivity of a positive linear functional plays a vital role in the argument. At last, we conclude that the crossed product A ⋊ H is a C * -algebra of finite dimension according to a faithful ∗- representation.

Suggested Citation

  • Xiaomin Wei & Lining Jiang & Dianlu Tian, 2021. "The Crossed Product of Finite Hopf C *-Algebra and C *-Algebra," Mathematics, MDPI, vol. 9(9), pages 1-9, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1023-:d:547494
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