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We introduce a family of three parameters 2-dimensional algebras representingelements in the Brauer group BQ(k,H_4) of Sweedler Hopf algebra H_4 over afield k. They allow us to describe the mutual intersection of the subgroupsarising from a quasitriangular or coquasitriangular structure. We alsointroduce a new subgroup of BQ(k,H_4) whose elements are represented byalgebras for which the two natural Z_2-gradings coincide. We construct an exactsequence relating this subgroup to the Brauer group of Nichols 8-dimensionalHopf algebra E(2) with respect to the quasitriangular structure attached to the2x2-matrix N with 1 in the (1,2)-entry and zero elsewhere.

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