Symplectic forms on six dimensional real solvable Lie algebras

Abstract

The author constructs the symplectic structures on real, solvable, nonnilpotent Lie algebras of dimension six. The work falls into two cases, when the algebra is decomposable into two lower dimensional ideals and when it is indecomposable with four dimensional nilradical. It remains to consider the indecomposable case when the nilradical has dimension five. Also given are the Mauer-Cartan equations of the indecomposable, solvable, non-nilpotent Lie algebras in dimension three and five and those of dimension six that have a four-dimensional nilradical.