# The Lie algebra associated with the lower central series of a right-angled Coxeter group

## TL;DR

This paper explores the structure of the Lie algebra associated with the lower central series of right-angled Coxeter groups, providing explicit combinatorial descriptions for initial factors.

## Contribution

It offers a new explicit combinatorial description of the first three factors of the lower central series for right-angled Coxeter groups.

## Key findings

- Explicit description of the first three factors of the lower central series.
- Connection established between the Lie algebra of the group and the graph Lie algebra.
- Enhanced understanding of the algebraic structure of right-angled Coxeter groups.

## Abstract

We study the lower central series of a right-angled Coxeter group $RC_K$ and the associated Lie algebra $L(RC_K)$. The latter is related to the graph Lie algebra $L_K$. We give an explicit combinatorial description of the first three consecutive factors of the lower central series of the group $RC_K$.