Pseudo-multiplicative unitaries on C*-modules generalize the multiplicative unitaries of Baaj and Skandalis , and are analogues of the pseudo-multiplicative unitaries on Hilbert spaces studied by Enock, Lesieur, Vallin , , . 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