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arXiv · 1810.12935

Three infinite families of reflection Hopf algebras

Luigi Ferraro·Ellen Kirkman·W. Frank Moore·Robert Won
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Abstract

Let $H$ be a semisimple Hopf algebra acting on an Artin-Schelter regular algebra $A$, homogeneously, inner-faithfully, preserving the grading on $A$, and so that $A$ is an $H$-module algebra. When the fixed subring $A^H$ is also AS regular, thus providing a generalization of the Chevalley-Shephard-Todd Theorem, we say that $H$ is a reflection Hopf algebra for $A$. We show that each of the semisimple Hopf algebras $H_{2n^2}$ of Pansera, and $\mathcal{A}_{4m}$ and $\mathcal{B}_{4m}$ of Masuoka is a reflection Hopf algebra for an AS regular algebra of dimension 2 or 3.

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Luigi Ferraro, Ellen Kirkman, W. Frank Moore, Robert Won. 2018-10-30. Three infinite families of reflection Hopf algebras. https://doi.org/10.1016/j.jpaa.2020.106315

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