Journal of Lie Theory 27 (2017), No. 1, 043--049
Copyright 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.