Pointed Hopf algebras over some sporadic simple groups

TL;DR

This paper investigates the structure of finite-dimensional complex pointed Hopf algebras over sporadic simple groups, showing that most such algebras are just group algebras, with some notable exceptions.

Contribution

It proves that for most sporadic simple groups, the only finite-dimensional pointed Hopf algebras are group algebras, except possibly for certain Fischer, Baby Monster, and Monster groups.

Findings

Most sporadic simple groups have only group algebra Hopf algebras.

Exceptions may include Fischer groups Fi22, Baby Monster B, and Monster M.

The result narrows down the classification of pointed Hopf algebras over these groups.

Abstract

Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monster B and the Monster M, is a group algebra.