On the subgroup structure of the full Brauer group of Sweedler Hopf algebra

Abstract

We introduce a three-parameter family of two-dimensional algebras representing elements in the Brauer group BQ(k,H 4) of Sweedler Hopf algebra H 4 over a field k. They allow us to describe the mutual intersection of the subgroups arising from a quasitriangular or coquasitriangular structure. We also define a new subgroup of BQ(k,H 4) and construct an exact sequence relating it to the Brauer group of Nichols 8-dimensional Hopf algebra with respect to the quasitriangular structure attached to the 2 × 2-matrix with 1 in the (1, 2)-entry and zero elsewhere.