An exact sequence for the Brauer group of a finite quantum group

AbstractIn this paper, we give a general method to compute the Brauer group of a finite quantum group, i.e., a faithfully projective coquasitriangular Hopf algebra over a commutative ring with unity. Let (H,R) be a finite quantum group with an R-matrix R on H⊗H. There exists a braided Hopf algebra HR in the braided monoidal category of right H-comodules [S. Majid, J. Pure Appl. Algebra 86 (1993) 187–221]. We construct a group Gal(HR) consisting of quantum commutative H∗R-bigalois objects and show that there is an exact sequence of group homomorphisms: 1→Br(k)→BC(k,H,R)→Gal(HR), where Br(k) is the usual Brauer group of k and BC(k,H,R) is the Brauer group of (H,R) with respect to the R-matrix R