On Pointed Hopf Algebras with Weyl Groups of exceptional type

Abstract

All -1-type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non -1-type pointed Hopf algebra with real $G(H)$ is infinite dimensional and every central quantum linear space over finite group is finite dimensional. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over Weyl groups of exceptional type are infinite dimensional.

arXiv comment44pages

References in corpus (6)

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• Root systems and Weyl groupoids for Nichols algebras
• Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One
• On pointed Hopf algebras associated with the symmetric groups
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Cited by in corpus (7)

• The character tables of centralizers in Weyl Group of $E_8$ II
• The character tables of centralizers in Sporadic Simple Groups of $\mathrm{HS}$ and $\mathrm{C}{\mathrm{o}}_3$
• The radicals of (Braided) Lie algebras
• Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis
• On Pointed Hopf Algebras with Sporadic Simple Groups $\mathrm{HS}$ and $Co3$
• The character tables of centralizers in Sporadic Simple Groups of $\mathrm{McL}$
• Topological K-Theory for Hilbert Scheme Analogs