Cohomology of N-Graded Lie Algebras of Maximal Class over Z(2)

摘要

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(o)) 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).