Graded Components of the Lie Algebra Associated with the Lower Central Series of a Right-Angled Coxeter Group

The lower central series of a right-angled Coxeter group $\mathrm {RC}_{\mathcal K}$ and the corresponding graded Lie algebra $L(\mathrm {RC}_{\mathcal K})$ 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 $L(\mathrm {RC}_{\mathcal K})$. A basis of the fourth graded component of $L(\mathrm {RC}_{\mathcal K})$ for groups with at most four generators is described.