Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sequence to compute the Brauer group of certain quasi-triangular Hopf
  algebras   A deeper understanding of recent computations of the Brauer group of Hopf
algebras is attained by explaining why a direct product decomposition for this
group holds and describing the non-interpreted factor occurring in it. For a
Hopf algebra $B$ in a braided monoidal category $\C$, and under certain
assumptions on the braiding (fulfilled if $\C$ is symmetric), we construct a
sequence for the Brauer group $\BM(\C;B)$ of $B$-module algebras, generalizing
Beattie's one. It allows one to prove that $\BM(\C;B) \cong \Br(\C) \times
\Gal(\C;B),$ where $\Br(\C)$ is the Brauer group of $\C$ and $\Gal(\C;B)$ the
group of $B$-Galois objects. We also show that $\BM(\C;B)$ contains a subgroup
isomorphic to $\Br(\C) \times \Hc(\C;B,I),$ where $\Hc(\C;B,I)$ is the second
Sweedler cohomology group of $B$ with values in the unit object $I$ of $\C$.
These results are applied to the Brauer group of a quasi-triangular Hopf
algebra that is a Radford biproduct $B \times H$, where $H$ is a usual Hopf
algebra over a field $K$, the Hopf subalgebra generated by the quasi-triangular
structure $\R$ is contained in $H$ and $B$ is a Hopf algebra in the category
${}_H\M$ of left $H$-modules. The Hopf algebras whose Brauer group was recently
computed fit this framework. We finally show that $\BM(K,H,\R) \times
\Hc({}_H\M;B,K)$ is a subgroup of the Brauer group $\BM(K,B \times H,\R),$
confirming the suspicion that a certain cohomology group of $B \times H$
(second lazy cohomology group was conjectured) embeds into $\BM(K,B \times
H,\R).$ New examples of Brauer groups of quasi-triangular Hopf algebras are
computed using this sequence.

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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an