Semisimple Reflection Hopf Algebras of Dimension Sixteen

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 $A$.

Revised version. To appear in Algebras and Representation Theory

References in corpus (1)

• Degree bounds for Hopf actions on Artin-Schelter regular algebras

Cited by in corpus (1)

• The Jacobian, reflection arrangement and discriminant for reflection Hopf algebras