
Journal of Lie Theory 27 (2017), No. 1, 043049 Copyright Heldermann Verlag 2017 On the Cohomology of FourDimensional 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 [Abstractpdf] \def\g{{\frak g}} It is shown that the unimodularity condition for a fourdimensional 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) 17141731]. This note proves the other direction. Keywords: 4dimensional Lie algebras, almost complex structure, cohomology decomposition. MSC: 17B56, 53C15 [ Fulltextpdf (216 KB)] for subscribers only. 