\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 $\Z_2$.
Classification :
17B56, 17B50, 17B70, 17B65, 17B30
Mots-clés :
Lie algebra of maximal class, characteristic 2, cohomology, Betti number
Affiliations des auteurs :
Yuri Nikolayevsky
1
;
Ioannis Tsartsaflis
1
1
Dept. of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia
Yuri Nikolayevsky; Ioannis Tsartsaflis. Cohomology of N-Graded Lie Algebras of Maximal Class over Z2. Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 529-544. http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a10/
@article{JOLT_2017_27_2_a10,
author = {Yuri Nikolayevsky and Ioannis 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a10/}
}
TY - JOUR
AU - Yuri Nikolayevsky
AU - Ioannis Tsartsaflis
TI - Cohomology of N-Graded Lie Algebras of Maximal Class over Z2
JO - Journal of Lie Theory
PY - 2017
SP - 529
EP - 544
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a10/
ID - JOLT_2017_27_2_a10
ER -
%0 Journal Article
%A Yuri Nikolayevsky
%A Ioannis Tsartsaflis
%T Cohomology of N-Graded Lie Algebras of Maximal Class over Z2
%J Journal of Lie Theory
%D 2017
%P 529-544
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a10/
%F JOLT_2017_27_2_a10
