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Cocycle Deformations and Brauer Group Isomorphisms

Huixiang Chen·Yinhuo Zhang
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Abstract

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

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Huixiang Chen, Yinhuo Zhang. 2005-04-30. Cocycle Deformations and Brauer Group Isomorphisms. https://arxiv.org/abs/math/0505003

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