Quasitriangular Hopf algebras of dimension pq^2

TL;DR

This paper classifies all non-simple quasitriangular Hopf algebras of dimension pq^2 over an algebraically closed field of characteristic zero, including their quasitriangular structures, where p and q are distinct odd primes.

Contribution

It provides a complete classification of such Hopf algebras and their quasitriangular structures, advancing understanding of their algebraic properties.

Findings

Classification of all non-simple quasitriangular Hopf algebras of dimension pq^2

Explicit description of all quasitriangular structures on these algebras

Results applicable to algebraic structures over fields of characteristic zero

Abstract

Let p and q be distinct odd primes and assume k is an algebraically closed field of characteristic zero. We classify all quasitriangular Hopf algebras of dimension pq^2 over k, which are not simple as Hopf algebras. Moreover, we obtained all quasitriangular structures on these Hopf algebras.