Journal of Siberian Federal University. Mathematics & Physics / On the Orbits of Nilpotent 7-dimensional Lie Algebras in 4-dimensional Complex Space

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Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (3)
Loboda, Alexander V.; Akopyan, Ripsime S.; Krutskikh, Vladislav V.
Contact information
Loboda, Alexander V.: Voronezh State Technical University Voronezh, Russian Federation; ; OCRID: 0000-0002-0285-5841; Akopyan, Ripsime S.: MIREA, Russian Technological University Moscow, Russian Federation; ; Krutskikh, Vladislav V.: Voronezh State University Voronezh, Russian Federation;
Lie algebra; complex space; vector field; holomorphic function; homogeneous variety; Levi degeneracy

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

Paper at repository of SibFU