On consecutive factors of the lower central series of right-angled Coxeter groups

Abstract

We study the lower central series of the right-angled Coxeter group $R{C}_{\mathcal{K}}$ and the corresponding associated graded Lie algebra $L(R{C}_{\mathcal{K}})$ and describe the basis of the fourth graded component of $L(R{C}_{\mathcal{K}})$ for any $\mathcal{K}$.