On the string Lie algebra

TL;DR

This paper constructs an abelian representative for the string Lie algebra's associated crossed module and applies it to define quasi-invariant tensors, advancing the categorification of infinitesimal braiding in g-modules.

Contribution

It introduces a novel abelian representative for the string Lie algebra's crossed module and uses it to define quasi-invariant tensors for categorifying infinitesimal braiding.

Findings

Constructed an abelian representative for the crossed module

Defined quasi-invariant tensors for categorification

Applied to the category of g-modules with an r-matrix

Abstract

We construct an abelian representative for the crossed module associated to the string Lie algebra. We show how to apply this construction in order to define quasi-invariant tensors which serve to categorify the infinitesimal braiding on the category of g-modules given by an r-matrix, following Cirio-Martins.