Constructing quasitriangular multiplier Hopf algebras by twisted tensor coproducts

Abstract

Let A and B be multiplier Hopf algebras, and let R is an element of M(B circle times A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux [5]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A circle times(R) B. Using this, we establish the correspondence between the existence of quasitriangular structures in A circle times(R) B and the existence of such structures in the factors A and B. We illustrate our theory with a profusion of examples which cannot be obtained by using classical Hopf algebras. Also, we study the class of minimal quasitriangular multiplier Hopf algebras and show that every minimal quasitriangular Hopf algebra is a quotient of a Drinfel'd double for some algebraic quantum group.