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

Abstract

The lower central series of the rgiht-angled Coxeter group $RC_\mathcal K$ and the corresponding graded Lie algebra $L(RC_\mathcal K)$ 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 $L(RC_\mathcal K)$. A basis of the fourth graded component $L(RC_\mathcal K)$ for groups with at most $4$ generators was described.