Cocycle Deformations and Brauer Group Isomorphisms
نویسنده
چکیده
Let H be a Hopf algebra over a commutative ring k with unity and σ : H ⊗ H −→ k be a cocycle on H. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra H 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). Moreover, the group Gal(HR) constructed in [19] is studied under a cocycle deformation.
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