Three infinite families of reflection Hopf algebras

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 Chevalle...

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Bibliographic Details
Published in:arXiv.org 2019-11
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: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.12935