Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 27 (2017), No. 1, 043--049Copyright Heldermann Verlag 2017 On the Cohomology of Four-Dimensional Almost Complex Lie Algebras Tedi Draghici Dept. of Mathematics, Florida International University, Miami, FL 33199, U.S.A. draghici@fiu.edu Hector Leon Dept. of Mathematics, Florida International University, Miami, FL 33199, U.S.A. hleon002@fiu.edu [Abstract-pdf] \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. Keywords: 4-dimensional Lie algebras, almost complex structure, cohomology decomposition. MSC: 17B56, 53C15 [ Fulltext-pdf  (216  KB)] for subscribers only.