Abstract:Realizations are studied for a particular block of 5-dimensional Lie algebras (within the well-known Mubarakzyanov classification) in the form of algebras of holomorphic vector fields on homogeneous real hypersurfaces of the 3-dimensional complex space. All (locally) holomorphically homogeneous and Levi nondegenerate real hypersurfaces associated with algebras in the block in question are described. A majority of such manifolds are holomorphic images of tubular hypersurfaces with affine homogeneous base. At the same time, two new holomorphically homogeneous hypersurfaces are obtained that do not reduce to tubes, have sign-indefinite Levi form, and are algebraic surfaces of degree .

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中文翻译：

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5维李代数的全纯实现

摘要：以3维复空间的齐次实超曲面上的全纯矢量场的代数形式，研究了特定的5维李代数块（在著名的Mubarakzyanov分类中）的实现。描述了与所讨论的块中的代数相关的所有（局部）全纯同构且Levi非退化的实超曲面。大多数这样的流形是具有仿射均匀底面的管状超曲面的全纯图像。同时，获得了两个新的全纯同质超曲面，它们不还原为管，具有符号不确定的李维形式，并且是度数的代数曲面。

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