International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 25-28, Pages 1477-1486
doi:10.1155/S016117120430236X

Twisted quantum doubles

Abstract

Using diagrammatic pictures of tensor contractions, we consider a Hopf algebra (Aop⊗ℛλA*)* twisted by an element ℛλ∈A*⊗Aop corresponding to a Hopf algebra morphism λ:A→A. We show that this Hopf algebra is quasitriangular with the universal R-matrix coming from ℛλ when λ2=idA, generalizing the quantum double construction which corresponds to the case λ=idA.