Journal of Lie Theory

no. 1
On the Cohomology of Four-Dimensional Almost Complex Lie Algebras
Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 43-49
\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.
DOI: 10.5802/jolt.932
Classification: 17B56, 53C15
Keywords: 4-dimensional Lie algebras, almost complex structure, cohomology decomposition 
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     author = {T. Draghici and H. Leon},
     title = {On the {Cohomology} of {Four-Dimensional} {Almost} {Complex} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {43--49},
     year = {2017},
     volume = {27},
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     doi = {10.5802/jolt.932},
     zbl = {1386.53031},
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T. Draghici; H. Leon. On the Cohomology of Four-Dimensional Almost Complex Lie Algebras. Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 43-49. doi: 10.5802/jolt.932

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