Constructing Quasitriangular Multiplier Hopf Algebras By Twisted Tensor Coproducts

Let A and B be multiplier Hopf algebras, and let R ∈ M(B ? A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux 5 Delvaux , L. ( 2004 ). Twisted tensor coproduct of multiplier Hopf (*)-algebras . J. Algebra 274 : 751 – 771 . Google Scholar]]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A ? _R  B. Using this, we establish the correspondence between the existence of quasitriangular structures in A ? _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.