nLab
lower central series

Given a group G, its lower central series is the inductively defined descending sequence

G=G 0G 1G 2G = G_0 \supset G_1\supset G_2\supset \ldots

in which G k=[G,G k1] is the subgroup generated by all commutators ghg 1h 1 where gG and hG k1.

Similarly, given a Lie algebra L, its lower central series is the inductively defined descending sequence of Lie subalgebras L=L 0L 1L 2 in which L k=[L,L k1] is the Lie subalgebra generated bt all commutators [l,h] where lL and hL k1.

Created on June 16, 2011 17:58:35 by Zoran Škoda (161.53.130.104)