Cocycle Deformations and Brauer Group Isomorphisms

Details Cocycle Deformations and Brauer Group Isomorphisms Cocycle Deformations and Brauer Group Isomorphisms

2005-04-30

arxiv.org/abs/math/0505003v1

Mathematics

Quantum Algebra

33 pages, no figures

Scientific paper

Let $H$ be a Hopf algebra over a commutative ring $k$ with unity and $\sigma:H\otimes H\longrightarrow k$ be a cocycle on $H$. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra $H^{\sigma}$ is equivalent to the Yetter-Drinfeld module category of $H$. As a result of the equivalence, the "quantum Brauer" group BQ$(k,H)$ is isomorphic to BQ$(k,H^{\sigma})$. Moreover, the group $\Gal(\HR)$ constructed in \cite{Z} is studied under a cocycle deformation.

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