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

2009/04/12 by Giovanna Carnovale, Carnovale, Giovanna, Juan Cuadra +1
Mathematics · #16K50 #16W30 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16K50 #msc:16W30

paper · pdf · doi:10.48550/arxiv.0904.1883

Final version, to appear in Israel Journal of Mathematics

arxiv created 2009/10/16 · arxiv updated 2009/12/01

Abstract

We introduce a family of three parameters 2-dimensional algebras representing elements in the Brauer group BQ(k,H₄) of Sweedler Hopf algebra H₄ 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,H₄) whose elements are represented by algebras for which the two natural Z₂-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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