Semisimple Reflection Hopf Algebras of Dimension Sixteen

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 subrin...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Ferraro, Luigi, Kirkman, Ellen, Moore, W Frank, Won, Robert
Format: Article
Language:English
Subjects:
Algebra
Reflection
Online Access:Get full text
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Summary: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 \(A\).
ISSN:2331-8422
DOI:10.48550/arxiv.1907.06763