Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type IV. Unipotent classes in Chevalley and Steinberg groups

TL;DR

This paper investigates unipotent classes in finite simple Chevalley and Steinberg groups, demonstrating that most do not support finite-dimensional Nichols algebras, with a potential exception in certain involution classes.

Contribution

It classifies unipotent classes in these groups regarding their support for finite-dimensional Nichols algebras, extending previous understanding in the field.

Findings

Most unipotent classes collapse, not supporting finite-dimensional Nichols algebras.

A possible exception exists for one class of involutions in PSU_n(2^m).

Provides a classification for unipotent classes in Chevalley and Steinberg groups.

Abstract

We show that all unipotent classes in finite simple Chevalley or Steinberg groups, different from PSL_n(q) and PSp_{2n}(q), collapse (i.e. are never the support of a finite-dimensional Nichols algebra), with a possible exception on one class of involutions in PSU_n(2^m).