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Journal of Siberian Federal University. Mathematics & Physics, 2020, Volume 13, Issue 3, Pages 360–372
DOI: https://doi.org/10.17516/1997-1397-2020-13-3-360-372
(Mi jsfu845)
 

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
Full-text PDF (133 kB) Citations (7)
References:
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.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00592_a
20-01-00497
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
Citation in format AMSBIB
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\by Alexander~V.~Loboda, Ripsime~S.~Akopyan, Vladislav~V.~Krutskikh
\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
\mathnet{http://mi.mathnet.ru/jsfu845}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-3-360-372}
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал Сибирского федерального университета. Серия "Математика и физика"
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