On the Exponential Maps and the Triangular 2-Chomology of Graded Lie Rings of Length Three

Extract

Let H be a group. We mean by an Af-series in H a decreasing series of subgroups H₁ = H, H₂…,H_n+1 = {e} such that the commutator xyx^-1y^-1 of two elements x and y respectively in H_i and H_j belongs to H_i+j, where H_s = {e} for s≥n + 1. We call n the length of the N-series (H_i). We mean by a graded Lie ring of length n a Lie ring which is a direct sum A₁ + … + -A_n of additive subgroups A₁…, A_n such that [A_i, A_j]⊂A_i+j, where A_s = {0} for s≥n + 1.