The mod 4 behaviour of total Lie algebra cohomology

We show that if L is a unimodular Lie algebra over a field of characteristic 1 2ne 2, then the dimension ssigma(L) of the total cohomology of L is a multiple of 4 when dim(L)not o 3dim(L)notequiv 3 (mod 4). However, contrary to a claim by Deninger and Singhof, we give an example of a rational nilpotent algebra L of dimension 15 with s(L)not o 0sigma(L)notequiv 0 (mod 4). Over fields of characteristic 2, we completely classify those algebras L with s(L)not o 0sigma(L)notequiv 0 (mod 4).