Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type II. Unipotent classes in symplectic groups

TL;DR

This paper investigates the dimensions of Nichols algebras associated with unipotent classes in symplectic groups over finite fields, establishing conditions under which these algebras are infinite-dimensional.

Contribution

It provides a criterion for unipotent classes in finite simple groups of Lie type and applies it to symplectic groups, advancing understanding of pointed Hopf algebras.

Findings

Most Nichols algebras over these groups are infinite-dimensional

A new criterion for unipotent classes in Lie type groups

Application to regular unipotent classes

Abstract

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective symplectic linear group over a finite field, corresponding to unipotent orbits, have infinite dimension. We give a criterium to deal with unipotent classes of general finite simple groups of Lie type and apply it to regular classes