A Class of Quasitriangular Group-cograded Multiplier Hopf Algebras

Abstract

For a multiplier Hopf algebra pairing $⟨A,B⟩$, we construct a class of group-cograded multiplier Hopf algebras $D(A,B)$, generalizing the classical construction of finite dimensional Hopf algebras introduced by Panaite and Staic Mihai. Furthermore, if the multiplier Hopf algebra pairing admits a canonical multiplier in $M(B\otimes A)$ we show the existence of quasitriangular structure on $D(A,B)$. As an application, some special cases and examples are provided.

17 pages