Quiver Approaches to Quasi-Hopf Algebras

TL;DR

This paper introduces a quiver-based framework for quasi-Hopf algebras, extending existing Hopf quiver theory and deriving key structural theorems in the quasi-Hopf context.

Contribution

It generalizes Hopf quiver theory to quasi-Hopf algebras and establishes foundational structure theorems like the quasi-Hopf Cartier and Cartier-Gabriel decomposition theorems.

Findings

Established a quiver setting for quasi-Hopf algebras

Derived the quasi-Hopf analogue of the Cartier theorem

Proved the quasi-Hopf Cartier-Gabriel decomposition theorem

Abstract

We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel decomposition theorem.