Twisted deformations vs. cocycle deformations for quantum groups

We study two deformation procedures for quantum groups — namely, quantum universal enveloping algebras — those realized as twist deformations (that modify the coalgebra structure, while keeping the algebra one), called “twisted quantum groups” (=TwQGp’s), and those realized as 2–cocycle deformations (that deform the algebra structure, but save the coalgebra one), called “multiparameter quantum groups” (=MpQG’s). Up to technicalities, we show that the two methods actually are equivalent, in that they eventually provide isomorphic outputs.