Complex, symplectic, and contact structures on low-dimensional lie groups

It is well known that on any Lie group, a left-invariant Riemannian structure can be defined. For other left-invariant geometric structures, for example, complex, symplectic, or contact structures, there are difficult obstructions for their existence, which have still not been overcome, although a lot of works were devoted to them. In recent years, substantial progress in this direction has been made; in particular, classification theorems for low-dimensional groups have been obtained. This paper is a brief review of left-invariant complex, symplectic, pseudo-Kählerian, and contact structures on low-dimensional Lie groups and classification results for Lie groups of dimension 4, 5, and 6. © 2015 Springer Science+Business Media, Inc.