Geodesic
Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 106-119

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We compute explicitly the adjoint cohomology of two $\mathbb N$-graded Lie algebras of maximal class (infinite-dimensional filiform Lie algebras) $\mathfrak m_0$ and $\mathfrak m_2$. It is known that up to an isomorphism there are only three $\mathbb N$-graded Lie algebras of 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 Fuchs. 
@article{TM_2008_263_a7,
     author = {D. V. Millionshchikov},
     title = {Cohomology of {Graded} {Lie} {Algebras} of {Maximal} {Class} with {Coefficients} in the {Adjoint} {Representation}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {106--119},
     publisher = {mathdoc},
     volume = {263},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_263_a7/}
}
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D. V. Millionshchikov. Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 106-119. http://geodesic.mathdoc.fr/item/TM_2008_263_a7/