On subsequences of quiddity cycles and Nichols algebras

TL;DR

This paper introduces a method for analyzing quiddity cycles and applies it to classify rank two affine Nichols algebras of diagonal type, advancing understanding in algebraic structures.

Contribution

It offers a new tool for local analysis of quiddity cycles and achieves a classification of specific Nichols algebras of diagonal type.

Findings

Developed a tool for local descriptions of quiddity cycles

Classified rank two affine Nichols algebras of diagonal type

Enhanced understanding of algebraic structures related to Nichols algebras

Abstract

We provide a tool to obtain local descriptions of quiddity cycles. As an application, we classify rank two affine Nichols algebras of diagonal type.