Journal of Lie Theory

no. 2
Cohomology of N-Graded Lie Algebras of Maximal Class over Z2
Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 529-544
\def\m{{\frak m}} \def\Z{{\Bbb Z}} 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 to 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 $\Z_2$.
DOI: 10.5802/jolt.957
Classification: 17B56, 17B50, 17B70, 17B65, 17B30
Keywords: Lie algebra of maximal class, characteristic 2, cohomology, Betti number 
@article{JOLT_2017_27_2_a10,
     author = {Y. Nikolayevsky and I. Tsartsaflis},
     title = {Cohomology of {N-Graded} {Lie} {Algebras} of {Maximal} {Class} over {Z\protect\textsubscript{2}}},
     journal = {Journal of Lie Theory},
     pages = {529--544},
     year = {2017},
     volume = {27},
     number = {2},
     doi = {10.5802/jolt.957},
     zbl = {1412.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.957/}
}
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Y. Nikolayevsky; I. Tsartsaflis. Cohomology of N-Graded Lie Algebras of Maximal Class over Z2. Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 529-544. doi: 10.5802/jolt.957

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