On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras
in Three-Dimensional Complex Space

J 2019

On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space

ATANOV, A.V.; Ilya KOSSOVSKIY a A.V. LOBODA

Základní údaje

Originální název

On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space

Autoři

ATANOV, A.V.; Ilya KOSSOVSKIY a A.V. LOBODA

Vydání

DOKLADY MATHEMATICS, NEW YORK, MAIK NAUKA/INTERPERIODICA/SPRINGER, 2019, 1064-5624

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10100 1.1 Mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.548

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/19:00113742

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

CR-MANIFOLDS

Štítky

rivok

Změněno: 11. 5. 2020 18:35, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Citovat

ATANOV, A.V.; Ilya KOSSOVSKIY a A.V. LOBODA. On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space. DOKLADY MATHEMATICS. NEW YORK: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2019, roč. 100, č. 1, s. 377-379. ISSN 1064-5624. Dostupné z: https://doi.org/10.1134/S1064562419040173.

@article{1648783,
   author = {Atanov, A.V. and Kossovskiy, Ilya and Loboda, A.V.},
   article_location = {NEW YORK},
   article_number = {1},
   doi = {https://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 a 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, roč.~100, č.~1, s.~377-379. ISSN~1064-5624. Dostupné z: https://doi.org/10.1134/S1064562419040173.

Přehled o publikaci