Normal Hopf subalgebras in cocycle deformations of finite groups


Let $G$ be a finite group and let $\pi\colon G \to G’$ 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 $L$.

Manuscripta Math. 125 (2008), no. 4, 501–514
César Galindo
Associate Professor of Mathematics

My research interests include representation theory, category theory and their applications to Mathematical-Physics.