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

The lower central series of the rgiht-angled Coxeter group $R{C}_{\mathcal{K}}$ and the corresponding graded Lie algebra $L(R{C}_{\mathcal{K}})$ associated with the lower central series of a right-angled Coxeter group are studied. Relations are obtained in the graded components of the Lie algebra $L(R{C}_{\mathcal{K}})$. A basis of the fourth graded component $L(R{C}_{\mathcal{K}})$ for groups with at most $4$ generators was described.