Journal of Lie Theory 27 (2017), No. 2, 529--544
Copyright Heldermann Verlag 2017
Cohomology of N-Graded Lie Algebras of Maximal Class over Z2
Yuri Nikolayevsky
Dept. of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia
Y.Nikolayevsky@latrobe.edu.au
Ioannis Tsartsaflis
Dept. of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia
itsartsaflis@students.latrobe.edu.au
[Abstract-pdf]
\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 $\Z_2$.
Keywords: Lie algebra of maximal class, characteristic 2, cohomology, Betti number.
MSC: 17B56, 17B50, 17B70, 17B65, 17B30
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