# On Drinfel'd associators

## TL;DR

This paper explores Drinfel'd associators, providing new interpretations and tools related to noncommutative evolution equations, with a focus on their role in braid group representations and asymptotic behaviors.

## Contribution

It offers a novel interpretation of Drinfel'd associators and introduces new tools involving noncommutative evolution equations.

## Key findings

- New interpretation of Drinfel'd associators
- Development of tools for noncommutative evolution equations
- Discussion of asymptotic phenomena related to associators

## Abstract

In 1986, in order to study the linear representations of the braid group $B\_n$coming from the monodromy of the Knizhnik-Zamolodchikov differential equations,Drinfel'd introduced a class of formal power series $\Phi$on noncommutative variables. These formal series can be considered as a class of associators. We here give an interpretation of them as well as some new tools over Noncommutative Evolution Equations. Asymptotic phenomena are also discussed.