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An Operator Algebraic Framework for the Duality of Quantum Groups

In: Mathematical Physics X

Author

Listed:
  • Tetsuya Masuda

    (University of Tsukuba, Institute of Mathematics)

  • Yoshiomi Nakagami

    (Yokohama City University, Department of Mathematics)

Abstract

The duality for a locally compact group established by Pontrjagin, Tannaka, Krein, Steinspring, Eymard and Tatsuuma is an important theoretical basis for the harmonic analysis. At the formal level of pure algebras, the notion of Hopf algebras is used to deal with the algebraic groups, discrete groups, or their dual objects at the same time. In order to control the infinite dimensional unitary representations, functional analysis is necessarily combined with the algebraic framework of Hopf algebras. This consideration suggests us to introduce the notion of Kac-algebras in the language of the Neumann algebras, in with the above mentioned duality is generalized by Kac [5], Takesaki [9] and Enock and Schwartz [2].

Suggested Citation

  • Tetsuya Masuda & Yoshiomi Nakagami, 1992. "An Operator Algebraic Framework for the Duality of Quantum Groups," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 291-295, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_24
    DOI: 10.1007/978-3-642-77303-7_24
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