Normal Hopf subalgebras in cocycle deformations of finite groups

Details Normal Hopf subalgebras in cocycle deformations of finite groups Normal Hopf subalgebras in cocycle deformations of finite groups

2007-08-24

arxiv.org/abs/0708.3407v3

Mathematics

Quantum Algebra

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Scientific paper

Let $G$ be a finite group and let $\pi: G \to G'$ be a surjective group homomorphism. Consider the cocycle deformation $L = H^{\sigma}$ of the Hopf algebra $H = k^G$ of $k$-valued linear functions on $G$, with respect to some convolution invertible 2-cocycle $\sigma$. The (normal) Hopf subalgebra $k^{G'} \subseteq k^G$ corresponds to a Hopf subalgebra $L' \subseteq L$. Our main result is an explicit necessary and sufficient condition for the normality of $L'$ in $L$.

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