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.
This work was supported by the Russian Foundation for Basic Research (projects no. 17-01-00592, 20-01-00497).
Received: 10.02.2020 Received in revised form: 10.03.2020 Accepted: 20.04.2020
Bibliographic databases:
Document Type:
Article
UDC:
517.765+512.816
Language: English
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
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\paper On the orbits of nilpotent 7-dimensional lie algebras in 4-dimensional complex space
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 3
\pages 360--372
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\crossref{https://doi.org/10.17516/1997-1397-2020-13-3-360-372}
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https://www.mathnet.ru/eng/jsfu845
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This publication is cited in the following 8 articles:
Vladislav Krutskikh, Alexandr Loboda, “APPLICATION OF SYSTEMS ANALYSIS AND COMPUTER ALGORITHMS IN STUDYING ORBITS OF 7-DIMENSIONAL LIE ALGEBRAS”, Mathematical Physics and Computer Simulation, 27:3 (2024), 38
A. V. Loboda, R. S. Akopyan, V. V. Krutskikh, “O 7-mernykh algebrakh golomorfnykh vektornykh polei v C4, imeyuschikh 5-mernyi abelev ideal”, Dalnevost. matem. zhurn., 23:1 (2023), 55–80
A. V. Loboda, “O 7-mernykh algebrakh Li, dopuskayuschikh Levi-nevyrozhdennye orbity v C4”, Tr. MMO, 84, no. 2, MTsNMO, M., 2023, 205–230
A.V. Atanov, A.V. Loboda, “On Degenerate Orbits of Real Lie Algebras in Multidimensional Complex Spaces”, Russ. J. Math. Phys., 30:4 (2023), 432
A. V. Atanov, “Orbits of decomposable 7-dimensional Lie algebras with sl(2) subalgebra”, Ufa Math. J., 14:1 (2022), 1–19
A. V. Loboda, V. K. Kaverina, “On degeneracy of orbits of nilpotent Lie algebras”, Ufa Math. J., 14:1 (2022), 52–76
A. V. Loboda, “On the Problem of Describing Holomorphically Homogeneous Real Hypersurfaces of Four-Dimensional Complex Spaces”, Proc. Steklov Inst. Math., 311 (2020), 180–198
A. V. Loboda, “Holomorphically homogeneous real hypersurfaces in C3”, Trans. Moscow Math. Soc., 81:2 (2020), 169–228
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