In the paper we describe the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of a residually solvable Leibniz algebra. It is proved that the second cohomology group of the extension is trivial.

中文翻译：

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无限维丝状莱布尼茨代数的剩余可解扩展

在论文中，我们描述了无限维丝状莱布尼茨代数的所有可解扩展的类。丝状莱布尼茨代数被视为剩余可解莱布尼茨代数的最大亲幂零理想。证明了扩展的第二个上同调群是平凡的。