Geodesic
On 7-dimensional algebras of holomorphic vector fields in $ \Bbb C^4 $,
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 55-80

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In connection with the problem of describing holomorphically homogeneous real hypersurfaces in $ \Bbb C^4 $ we study in this article the 7-dimensional orbits of real Lie algebras in this space. By the well-known Morozov theorem, any nilpotent 7-dimensional Lie algebra has at least a 4-dimensional Abelian ideal. The article considers nilpotent indecomposable 7-dimensional Lie algebras containing a 5-dimensional Abelian ideal. It is proved that in the space $ \Bbb C^4 $ all the orbits of such algebras are Levi degenerate. This statement covers 73 algebras from the complete list of 149 indecomposable 7-dimensional nilpotent Lie algebras. 
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     title = {On 7-dimensional algebras of holomorphic vector fields in $ \Bbb C^4 $,},
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A. V. Loboda; R. S. Akopyan; V. V. Krutskikh. On 7-dimensional algebras of holomorphic vector fields in $ \Bbb C^4 $,. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 55-80. http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a5/