Normal Hopf subalgebras in cocycle deformations of finite groups

Abstract

Let $G$ be a finite group and let $\pi :G\to G^{\prime }$ 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 $k^{G^{\prime }}\subseteq k^G$ corresponds to a Hopf subalgebra $L^{\prime }\subseteq L$. Our main result is an explicit necessary and sufficient condition for the normality of $L^{\prime }$ in $L$.

Final version

References in corpus (1)

• Simple Hopf algebras and deformations of finite groups