On the Notion of a Ribbon Quasi-Hopf Algebra

TL;DR

This paper proves the equivalence of two definitions of ribbon quasi-Hopf algebras and offers a new perspective on the Drinfel'd element to derive its key properties.

Contribution

It establishes the equivalence of competing definitions and provides a novel approach to understanding the Drinfel'd element in ribbon quasi-Hopf algebras.

Findings

Two definitions of ribbon quasi-Hopf algebra are shown to be equivalent.

A new perspective on the Drinfel'd element leads to fundamental property derivations.

Enhanced understanding of the structure of ribbon quasi-Hopf algebras.

Abstract

We show that two competing definitions of a ribbon quasi-Hopf algebra are actually equivalent. Along the way, we look at the Drinfel'd element from a new perspective and use this viewpoint to derive its fundamental properties.