Classification of quasi-affine Generalized Dynkin Diagrams with Rank $ 4$

TL;DR

This paper classifies all quasi-affine connected Generalized Dynkin Diagrams and Nichols algebras of rank 4, providing a comprehensive understanding of their structure and properties.

Contribution

It systematically identifies all quasi-affine Dynkin diagrams and Nichols algebras of rank 4, filling a gap in the classification of these algebraic structures.

Findings

Complete list of quasi-affine connected Dynkin diagrams of rank 4

Classification of quasi-affine Nichols algebras of rank 4

New insights into the structure of Lie braided algebras

Abstract

All quasi-affine connected Generalized Dynkin Diagram with rank $= 4$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $ 4$ are also found.