On pointed Hopf algebras associated with the symmetric groups II

TL;DR

This paper investigates the dimensions of Nichols algebras over symmetric groups, establishing that most are infinite-dimensional except for specific cases related to transpositions and certain classes in S_5.

Contribution

It extends previous work by classifying which Nichols algebras over symmetric groups are finite-dimensional, identifying exceptions related to transpositions and particular classes.

Findings

Most Nichols algebras over S_m (m > 4) are infinite-dimensional.

Finite-dimensional cases are limited to specific conjugacy classes.

Identifies potential exceptions in S_5 related to class (2,3).

Abstract

This is a sequel to arXiv:0807.2406. It is shown that the Nichols algebras over the symmetric groups S_m, m > 4, are all infinite-dimensional, except (maybe) those related to the transpositions considered by Fomin and Kirillov, resp. Milinski and Schneider, and the class of type (2,3) in S_5.