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Three infinite families of reflection Hopf algebras
- Publication Year :
- 2018
-
Abstract
- 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.<br />Comment: Some minor corrections
- Subjects :
- Mathematics - Rings and Algebras
16T05, 16E65, 16G10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1810.12935
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jpaa.2020.106315