On quiver-theoretic description for quasitriangularity of Hopf algebras

TL;DR

This paper explores the quasitriangularity of Hopf algebras using quiver theory, providing a combinatorial classification of coquasitriangular Hopf algebras, especially finite-dimensional pointed ones over algebraically closed fields of characteristic zero.

Contribution

It introduces a quiver-theoretic framework to classify coquasitriangular Hopf algebras, offering a complete finite-dimensional classification in characteristic zero.

Findings

Characterization of Hopf quivers for coquasitriangular structures

Complete classification of finite-dimensional coquasitriangular pointed Hopf algebras

Development of a combinatorial approach to Hopf algebra quasitriangularity

Abstract

This paper is devoted to the study of the quasitriangularity of Hopf algebras via Hopf quiver approaches. We give a combinatorial description of the Hopf quivers whose path coalgebras give rise to coquasitriangular Hopf algebras. With a help of the quiver setting, we study general coquasitriangular pointed Hopf algebras and obtain a complete classification of the finite-dimensional ones over an algebraically closed field of characteristic 0.