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@article{1648783,
author = {Atanov, A.V. and Kossovskiy, Ilya and Loboda, A.V.},
article_location = {NEW YORK},
article_number = {1},
doi = {http://dx.doi.org/10.1134/S1064562419040173},
keywords = {CR-MANIFOLDS},
language = {eng},
issn = {1064-5624},
journal = {DOKLADY MATHEMATICS},
title = {On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space},
url = {https://link.springer.com/article/10.1134/S1064562419040173},
volume = {100},
year = {2019}
}
TY - JOUR
ID - 1648783
AU - Atanov, A.V. - Kossovskiy, Ilya - Loboda, A.V.
PY - 2019
TI - On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space
JF - DOKLADY MATHEMATICS
VL - 100
IS - 1
SP - 377-379
EP - 377-379
PB - MAIK NAUKA/INTERPERIODICA/SPRINGER
SN - 10645624
KW - CR-MANIFOLDS
UR - https://link.springer.com/article/10.1134/S1064562419040173
L2 - https://link.springer.com/article/10.1134/S1064562419040173
N2 - In 1932, E. Cartan described holomorphically homogeneous real hypersurfaces of two-dimensional complex spaces, but a similar study in the three-dimensional case remains incomplete. In a series of works performed by several international teams, the problem is reduced to describing homogeneous surfaces that are nondegenerate in the sense of Levi and have exactly 5-dimensional Lie algebras of holomorphic vector fields. In this paper, precisely such homogeneous surfaces are investigated. At the same time, a significant part of the extensive list of abstract 5-dimensional Lie algebras does not provide new examples of homogeneity. Given in this paper, the complete description of the orbits of 5-dimensional non-solvable Lie algebras in a three-dimensional complex space includes examples of new homogeneous hypersurfaces. These results bring us closer to the completion of a large-scale scientific study that is of interest in various branches of mathematics.
ER -
ATANOV, A.V., Ilya KOSSOVSKIY and A.V. LOBODA. On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space. \textit{DOKLADY MATHEMATICS}. NEW YORK: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2019, vol.~100, No~1, p.~377-379. ISSN~1064-5624. Available from: https://dx.doi.org/10.1134/S1064562419040173.
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