Israel Journal of Mathematics

, Volume 183, Issue 1, pp 61–92 | Cite as

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

Article
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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.

Keywords

Hopf Algebra Group Morphism Module Algebra Central Simple Algebra Drinfeld Module 
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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura ed ApplicataPaduaItaly
  2. 2.Dpto. Álgebra y Análisis MatemáticoUniversidad de AlmeríaAlmeríaSpain

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