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This article is cited in 7 scientific papers (total in 7 papers)
On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space
Alexander V. Lobodaa, Ripsime S. Akopyanb, Vladislav V. Krutskikhc a Voronezh State Technical University, Voronezh, Russian Federation
b MIREA, Russian Technological University, Moscow, Russian Federation
c Voronezh State University, Voronezh, Russian Federation
Abstract:
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.
Received: 10.02.2020 Received in revised form: 10.03.2020 Accepted: 20.04.2020
Citation:
Alexander V. Loboda, Ripsime S. Akopyan, Vladislav V. Krutskikh, “On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space”, J. Sib. Fed. Univ. Math. Phys., 13:3 (2020), 360–372
Linking options:
https://www.mathnet.ru/eng/jsfu845 https://www.mathnet.ru/eng/jsfu/v13/i3/p360
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