Centralizers in partially commutative Lie algebras (Q1936283)

If \(G\) is any graph with the finite set of vertices \(X\) and \(R\) is any integral domain, then a partially commutative Lie \(R\)-algebra associated with \(G\) is any Lie algebra \({\mathcal L}\) with a finite set of generators \(\{A_x\}_{x\in X}\) satisfying the commutation relations \([A_x,A_y]=0\) whenever \(xy\) is an edge of \(G\). The main results of the paper under review provide descriptions of centralizers of elements of such a Lie algebra \({\mathcal L}\) in terms of the generators \(\{A_x\}_{x\in X}\).