The Brauer group of some quasitriangular Hopf algebras

We show that the Brauer group BM(k,Hν,Rs,β) of the quasitriangular Hopf algebra (Hν,Rs,β) is a direct product of the additive group of the field k and the classical Brauer group Bθs(k,Z2ν) associated to the bicharacter θs on Z2ν defined by θs(x,y)=ωsxy, with ω a 2νth root of unity.