A survey on multiplier Hopf algebras (Q2762047)

Multiplier Hopf algebras were introduced by the first author [Trans. Am. Math. Soc. 342, No. 2, 917-932 (1994; Zbl 0809.16047)] as a natural generalization of Hopf algebras in the case where the underlying algebra does not necessarily has unit. The \(k\)-functions on an infinite group with finite support was the motivating example. In the present survey, the situation of the theory is developed. After presenting the basic results in Section 1, the theory of multiplier Hopf algebras with integrals is considered. Actions and smash products are studied in Section 3. Next, the authors investigate the pairing of multiplier Hopf algebras and present a very concrete example deforming the algebra of polynomial functions on the \(ax+b\)-group. The paper finishes with the theory of corepresentations of multiplier Hopf algebras.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00024].