On left-invariant semi-Kähler structures on six-dimensional nilpotent nonsymplectic Lie groups

It is known that there are 34 classes of six-dimensional nilpotent Lie groups, many of which admit left-invariant symplectic and complex structures. Among them there are three classes of groups on which there are no left-invariant symplectic structures, but there are complex structures. In this work, semi-Kähler and almost para-semi-Kähler structures are defined on such Lie groups and their geometric properties are studied.