Rank 4 Nichols Algebras of Pale Braidings

TL;DR

This paper classifies certain finite Gelfand-Kirillov dimension Nichols algebras of rank 4 that are constructed from Yetter-Drinfeld modules over abelian groups, excluding decomposable cases.

Contribution

It provides a classification of rank 4 Nichols algebras with finite GK dimension that are indecomposable and arise from abelian group modules.

Findings

Complete classification of rank 4 Nichols algebras with finite GK dimension

Identification of conditions for indecomposability in these algebras

Extension of known classifications to a new rank and setting

Abstract

We classify finite GK-dimensional Nichols algebras ${\mathscr B}(V)$ of rank 4 such that $V$ arises as a Yetter-Drinfeld module over an abelian group but it is not a direct sum of points and blocks.