Almost Kähler 4-dimensional Lie groups with \(J\)-invariant Ricci tensor (Q2486074)

The goal of this paper is to determine the left-invariant strictly almost Kähler structures with \(J\)-invariant Ricci tensor on real \(4\)-dimensional Lie groups. The author proves that a Lie group admitting such a structure is necessarily solvable, hence its commutator is of dimension at most \(3\), and she gives a general description of its Lie algebra. Moreover, she shows that all these Lie groups are isometric (up to homothety) to the (unique) \(4\)-dimensional proper \(3\)-symmetric space described by [\textit{O. Kowalski}, Generalized Symmetric Spaces. Lecture Notes in Mathematics. 805. (Berlin: Springer-Verlag). (1980; Zbl 0431.53042)].