We compute the cohomology with trivial coefficients of Lie algebras m 0 and m 2 of maximal class over the field Z 2 .In the infinite-dimensional case, we show that the cohomology rings H * (m 0 ) and H * (m 2 ) are isomorphic, in contrast with the case of the ground field of characteristic zero, and we obtain a complete description of them.In the finite-dimensional case, we find the first three Betti numbers of m 0 (n) and m 2 (n) over Z 2 .
Nikolayevsky et al. (Sun,) studied this question.