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

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