We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kahler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence of Vaisman structures and we establish some relations with other geometric notions, such as Sasakian, coKahler and left-symmetric algebra structures. Applying these results we construct families of Lie algebras and Lie groups admitting a Vaisman structure and we show the existence of lattices in some of these families, obtaining in this way many examples of new solvmanifolds equipped with invariant Vaisman structures.

中文翻译：

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Vaisman 求解流形和与其他几何结构的关系

我们根据配备适当推导的 Kahler 平面李代数来表征具有 Vaisman 结构的单模可解李代数。使用这种表征，我们获得了 Vaisman 结构存在的代数限制，并建立了与其他几何概念的一些关系，例如 Sasakian、coKahler 和左对称代数结构。应用这些结果，我们构造了李代数和李群的族，该族允许维斯曼结构，并且我们证明了其中一些族中格的存在，以这种方式获得了许多配备不变维斯曼结构的新求解流形的例子。