A lot of quasitriangular group-cograded multiplier Hopf algebras.
Group cograded multiplier Hopf algebras and the quasitriangular condition on them were defined by \textit{A. T. Abd El-Hafez, L. Delvaux} and \textit{A. Van Daele} [Algebr. Represent. Theory 10, No. 1, 77-95 (2007; Zbl 1129.16027)] and \textit{L. Delvaux, A. Van Daele} and \textit{S.-H. Wang} [J. Algebra 289, No. 2, 484-514 (2005; Zbl 1079.16022)]. The aim of the paper under review is to construct new examples of quasitriangular group-cograded multiplier Hopf algebras. For this purpose, it is introduced the concept of a \(\sigma\)-compatible pairing associated to regular multiplier Hopf algebras \(A\) and \(B\), and to a multiplier Hopf dual pairing \(\sigma\). In such a framework, a twisted double group-cograded multiplier Hopf algebra is constructed, and it is shown that it has a quasitriangular structure in the case where there is a canonical multiplier in \(M(B\otimes A)\). Examples in the particular case of usual Hopf algebras are given to illustrate the construction.
quasitriangular multiplier Hopf algebras
scientific article; zbMATH DE number 6052421
scientific article