Classification of quasi-affine Generalized Dynkin Diagrams with Rank $3$ and Rank $2$

TL;DR

This paper classifies all quasi-affine Generalized Dynkin Diagrams and Nichols algebras with ranks 2 and 3, providing a comprehensive understanding of their structures.

Contribution

It systematically determines all quasi-affine Dynkin diagrams and Nichols algebras for ranks 2 and 3, filling a gap in the classification theory.

Findings

Complete list of quasi-affine Dynkin diagrams for ranks 2 and 3.

Complete classification of Nichols (Lie braided) algebras for ranks 2 and 3.

New structural insights into low-rank quasi-affine algebraic objects.

Abstract

All quasi-affine connected Generalized Dynkin Diagram with rank $= 3$ and $2$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $ 3$ and $2$ are also found.