Geodesic
On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 360-372

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We study one-parameter families of 7-dimensional nilpotent indecomposable Lie algebras and the orbits of holomorphic realizations of such algebras in a 4-dimensional complex space. It is shown, in contrast to the orbits of 5-dimensional nilpotent Lie algebras in 3-dimensional case, that two such families (out of the existing nine ones) admit orbits that are Levi non-degenerate (homogeneous) real non-spherical hypersurfaces. Up to holomorphic equivalence, all obtained non-degenerate nonspherical orbits are graphs of polynomials of degree 4.
Keywords: Lie algebra, complex space, vector field, holomorphic function, homogeneous variety, Levi degeneracy. 
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     title = {On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space},
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     language = {en},
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Alexander V. Loboda; Ripsime S. Akopyan; Vladislav V. Krutskikh. On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 360-372. http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a9/