JournalsjncgVol. 1, No. 4pp. 497–542

Pseudo-multiplicative unitaries on C*-modules and Hopf C*-families I

  • Thomas Timmermann

    University of Münster
Pseudo-multiplicative unitaries on C*-modules and Hopf C*-families I cover
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Abstract

Pseudo-multiplicative unitaries on C*-modules generalize the multiplicative unitaries of Baaj and Skandalis [1], and are analogues of the pseudo-multiplicative unitaries on Hilbert spaces studied by Enock, Lesieur, Vallin [5], [10], [21]. We introduce Hopf C*-families on C*-bimodules and associate to special classes of pseudo-multiplicative unitaries two Hopf C*-families. Furthermore, we discuss dual pairings and counits on these Hopf C*-families, étalé and proper pseudo-multiplicative unitaries, and two classes of examples. In a later article, we will study regularity conditions on pseudo-multiplicative unitaries, coactions of Hopf C*-families on C*-algebras, and duality.

Cite this article

Thomas Timmermann, Pseudo-multiplicative unitaries on C*-modules and Hopf C*-families I. J. Noncommut. Geom. 1 (2007), no. 4, pp. 497–542

DOI 10.4171/JNCG/14