Cocycle twisting of E(n)-module algebras and applications to the Brauer group

Details Cocycle twisting of E(n)-module algebras and applications to the Brauer group Cocycle twisting of E(n)-module algebras and applications to the Brauer group

2004-03-25

arxiv.org/abs/math/0403444v2

Mathematics

Representation Theory

Accidentally an old version of the paper was posted. Main corrections are in Section 2 and in Section 4.2

Scientific paper

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group $BQ(k,E(n))$ of E(n) that are isomorphic. For a triangular structure $R$ on E(n) we prove that the subgroup $BM(k,E(n),R)$ of $BQ(k,E(n))$ arising from $R$ is isomorphic to a direct product of $BW(k)$, the Brauer-Wall group of the ground field $k$, and $Sym_n(k)$, the group of $n \times n$ symmetric matrices under addition. For a general quasi-triangular structure $R'$ on E(n) we construct a split short exact sequence having $BM(k,E(n), R')$ as a middle term and as a left term a central extension of the group of symmetric matrices of order $r

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