2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138097We compute explicitly the adjoint cohomology of two N-graded Lie algebras of maximal class (infinite dimensional filiform Lie algebras) m_0 and m_2. It is known that up to an isomorphism there are only three N-graded Lie algebras of the maximal class. The third algebra from this list is the "positive" part L_1 of the Witt (or Virasoro) algebra and its adjoint cohomology was computed earlier by Feigin and Fukhs. We show that the total space H*(m_j,m_j) is "almost" isomorphic to the completed tensor product of the algebra m_j by scalar cohomology space H^*(m_j), j=0,2.Rings and AlgebrasRepresentation Theory17B56; 17B70text