Cocycle twisting of E(n)-module algebras and applications to the Brauer group
نویسندگان
چکیده
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 AutHopf (E(n)). Using this result we show that for any triangular structure R on E(n) the Brauer group BM(k,E(n), R) is the direct product of the Brauer-Wall group of the base field k and the group Symn(k) of symmetric matrices of order n with entries in k under addition. If R′ is a quasi-triangular structure on E(n) we provide a short exact sequence having the group BM(k,E(n), R′) as middle term and with kernel an explicit central extension of the group of symmetric matrices of order r < n (with r depending on R′). Finally, we compute the map from the semi-direct product of Symn(k)⋊ AutHopf (E(n)) to BQ(k,E(n)) and its kernel.
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