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

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

2009-04-12

arxiv.org/abs/0904.1883v2

Mathematics

Rings and Algebras

Final version, to appear in Israel Journal of Mathematics

Scientific paper

We introduce a family of three parameters 2-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 introduce a new subgroup of BQ(k,H_4) whose elements are represented by algebras for which the two natural Z_2-gradings coincide. We construct an exact sequence relating this subgroup to the Brauer group of Nichols 8-dimensional Hopf algebra E(2) with respect to the quasitriangular structure attached to the 2x2-matrix N with 1 in the (1,2)-entry and zero elsewhere.

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