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Co-Involutive Hopf-Von Neumann Algebras

In: Kac Algebras and Duality of Locally Compact Groups

Author

Listed:
  • Michel Enock

    (Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales)

  • Jean-Marie Schwartz

    (Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales)

Abstract

This chapter is devoted to the structure of co-involutive Hopf-von Neumann algebras, which has been introduced by Ernest ([44]), and mostly studied by Kirchberg ([79]), and de Cannière and the authors ([21]). The paradigm, from which the whole theory comes, is the algebra L ∞(G) of all the (classes of) essentially bounded measurable (with respect to a left Haar measure) complex valued functions on a locally compact group G,equipped with a coproduct and a co-involution, which are nothing but the duals of the usual product and involution of the involutive Banach algebra L 1 (G) of all (classes of) integrable (with respect to a left Haar measure) complex valued functions on G (let us recall that L l (G) is the predual of L ∞(G)).

Suggested Citation

  • Michel Enock & Jean-Marie Schwartz, 1992. "Co-Involutive Hopf-Von Neumann Algebras," Springer Books, in: Kac Algebras and Duality of Locally Compact Groups, chapter 0, pages 7-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-02813-1_2
    DOI: 10.1007/978-3-662-02813-1_2
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