Geodesic
Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation
Informatics and Automation, 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{TRSPY_2008_263_a7,
     author = {D. V. Millionshchikov},
     title = {Cohomology of {Graded} {Lie} {Algebras} of {Maximal} {Class} with {Coefficients} in the {Adjoint} {Representation}},
     journal = {Informatics and Automation},
     pages = {106--119},
     publisher = {mathdoc},
     volume = {263},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/}
}
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D. V. Millionshchikov. Cohomology of Graded Lie Algebras of Maximal Class with Coefficients in the Adjoint Representation. Informatics and Automation, Geometry, topology, and mathematical physics. I, Tome 263 (2008), pp. 106-119. http://geodesic.mathdoc.fr/item/TRSPY_2008_263_a7/