Finite quasi-quantum groups of rank two

TL;DR

This paper classifies finite-dimensional connected graded pointed Majid algebras of rank two, expanding the understanding of finite pointed quasi-quantum groups beyond traditional Hopf algebra structures.

Contribution

It provides a complete classification of rank two finite-dimensional pointed Majid algebras that are not twist equivalent to Hopf algebras, advancing the structure theory of quasi-quantum groups.

Findings

Classified all rank two finite-dimensional connected graded pointed Majid algebras.

Identified those not twist equivalent to ordinary Hopf algebras.

Enhanced the understanding of the structure of finite pointed quasi-quantum groups.

Abstract

This is a contribution to the structure theory of finite pointed quasi-quantum groups. We classify all finite-dimensional connected graded pointed Majid algebras of rank two which are not twist equivalent to ordinary pointed Hopf algebras.