Kustermans, J.; Van Daele, A. \(C^*\)-algebraic quantum groups arising from algebraic quantum groups. (English) Zbl 1009.46038 Int. J. Math. 8, No. 8, 1067-1139 (1997). From the introduction: The main purpose of this paper is the construction of a \(C^*\)-algebraic quantum group (in the sense of Masuda, Nakagami and Woronowicz (unpublished)) out of a multiplier Hopf \(*\)-algebra which possesses a positive left-invariant functional. In the first section we give an overview of the results of van Daele about such multiplier Hopf \(*\)-algebras. In the second section we introduce the \(C^*\)-algebra together with the comultiplication. From there on, we gradually prove that this \(C^*\)-algebra fits almost in the scheme of Masuda, Nakagami and Woronowicz.Multiplier Hopf algebras have been introduced by A. Van Daele [Trans. Am. Math. Soc. 342, 917-932 (1994; Zbl 0809.16047)] as a generalisation of Hopf algebras to the case of nonunital algebras. Cited in 1 ReviewCited in 27 Documents MathOverflow Questions: Relating different definitions of dual of a compact quantum group MSC: 46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory 17B37 Quantum groups (quantized enveloping algebras) and related deformations 46L05 General theory of \(C^*\)-algebras 16W30 Hopf algebras (associative rings and algebras) (MSC2000) Citations:Zbl 0809.16047 PDFBibTeX XMLCite \textit{J. Kustermans} and \textit{A. Van Daele}, Int. J. Math. 8, No. 8, 1067--1139 (1997; Zbl 1009.46038) Full Text: DOI arXiv