\def\g{{\frak g}} It is shown that the unimodularity condition for a four-dimensional Lie algebra $\g$ with $H^2(\g) \neq \{0\}$ is equivalent with a certain decomposition of the group $H^2(\g)$ taking place with respect to any almost complex structure $J$ on $\g$. One direction of this result was proved by T.-J. Li and A. Tomassini [``Almost K\"ahler structures on four dimensional unimodular Lie algebras'', J. Geom. Phys. 62 (2012) 1714--1731]. This note proves the other direction.
1
Dept. of Mathematics, Florida International University, Miami, FL 33199, U.S.A.
Tedi Draghici; Hector Leon. On the Cohomology of Four-Dimensional Almost Complex Lie Algebras. Journal of Lie Theory, Tome 27 (2017) no. 1, pp. 43-49. http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a1/
@article{JOLT_2017_27_1_a1,
author = {Tedi Draghici and Hector Leon},
title = {On the {Cohomology} of {Four-Dimensional} {Almost} {Complex} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {43--49},
year = {2017},
volume = {27},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a1/}
}
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AU - Tedi Draghici
AU - Hector Leon
TI - On the Cohomology of Four-Dimensional Almost Complex Lie Algebras
JO - Journal of Lie Theory
PY - 2017
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EP - 49
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IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_1_a1/
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