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Semisimple Reflection Hopf Algebras of Dimension Sixteen

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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 AH is determined. When AH 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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Acknowledgments

We appreciate the careful reading of the manuscript by the referee who caught several mistakes and suggested a simplification of our arguments for inner-faithfulness, which we have adopted.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409, USA

    Luigi Ferraro

  2. Department of Mathematics and Statistics, Wake Forest University, P. O. Box 7388, Winston-Salem, NC, 27109, USA

    Ellen Kirkman & W. Frank Moore

  3. Department of Mathematics, University of Washington, Box 354350, Seattle, Washington, 98195, USA

    Robert Won

Authors
  1. Luigi Ferraro
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  2. Ellen Kirkman
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  3. W. Frank Moore
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  4. Robert Won
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Correspondence to Luigi Ferraro.

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Presented by: Michel Van den Bergh

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Ferraro, L., Kirkman, E., Moore, W.F. et al. Semisimple Reflection Hopf Algebras of Dimension Sixteen. Algebr Represent Theor 25, 615–647 (2022). https://doi.org/10.1007/s10468-021-10038-w

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  • DOI: https://doi.org/10.1007/s10468-021-10038-w

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