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arXiv · 1907.06763

Semisimple Reflection Hopf Algebras of Dimension Sixteen

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

For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over $\mathbb{C}$, the smallest dimension inner-faithful representation of $H$ acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously and preserving the grading, is determined. Each invariant subring $A^H$ is determined. When $A^H$ is also AS regular, thus providing a generalization of the Chevalley-Shephard-Todd Theorem, we say that $H$ is a reflection Hopf algebra for $A$.

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Luigi Ferraro, Ellen Kirkman, W. Frank Moore, Robert Won. 2019-07-15. Semisimple Reflection Hopf Algebras of Dimension Sixteen. https://doi.org/10.1007/s10468-021-10038-w

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