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arXiv · 1508.01251

Finite dimensional Hopf actions on central division algebras

Juan Cuadra·Pavel Etingof
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Abstract

Let $\mathbb{k}$ be an algebraically closed field of characteristic zero. Let $D$ be a division algebra of degree $d$ over its center $Z(D)$. Assume that $\mathbb{k}\subset Z(D)$. We show that a finite group $G$ faithfully grades $D$ if and only if $G$ contains a normal abelian subgroup of index dividing $d$. We also prove that if a finite dimensional Hopf algebra coacts on $D$ defining a Hopf-Galois extension, then its PI degree is at most $d^2$. Finally, we construct Hopf-Galois actions on division algebras of twisted group algebras attached to bijective cocycles.

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Juan Cuadra, Pavel Etingof. 2015-08-06. Finite dimensional Hopf actions on central division algebras. https://arxiv.org/abs/1508.01251

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