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Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds. / Taimanov, I. A.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 327, No. 1, 12.2024, p. 300-312.

Research output: Contribution to journal › Article › peer-review

Harvard

Taimanov, IA 2024, 'Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds', Proceedings of the Steklov Institute of Mathematics, vol. 327, no. 1, pp. 300-312. https://doi.org/10.1134/S0081543824060221

APA

Taimanov, I. A. (2024). Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds. Proceedings of the Steklov Institute of Mathematics, 327(1), 300-312. https://doi.org/10.1134/S0081543824060221

Vancouver

Taimanov IA. Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds. Proceedings of the Steklov Institute of Mathematics. 2024 Dec;327(1):300-312. doi: 10.1134/S0081543824060221

Author

Taimanov, I. A. / Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds. In: Proceedings of the Steklov Institute of Mathematics. 2024 ; Vol. 327, No. 1. pp. 300-312.

BibTeX

@article{04ac30468bdc402ab55421be2a6eb4e5,
title = "Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds",
abstract = "We describe the relations between Euler{\textquoteright}s equations on central extensions of Lie algebras and Euler{\textquoteright}s equations on the original algebras that we extend. We consider a special infinite sequence of central extensions of nilpotent Lie algebras constructed from the Lie algebra of formal vector fields on the line, and describe the orbits of coadjoint representations for these algebras. By using the compact nilmanifolds constructed from these algebras by I. K. Babenko and the author, we show that the covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.",
keywords = "Euler equations on Lie algebras, central extensions of Lie algebras, geodesic flows, magnetic geodesic flows, orbits of coadjoint representations of nilpotent Lie groups, symplectic nilmanifolds",
author = "Taimanov, {I. A.}",
note = "This work was supported by the Russian Science Foundation under grant no. 24-11-00281, https://rscf.ru/en/project/24-11-00281/.",
year = "2024",
month = dec,
doi = "10.1134/S0081543824060221",
language = "English",
volume = "327",
pages = "300--312",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "ФГБУ {"}Издательство {"}Наука{"}",
number = "1",

}

RIS

TY - JOUR

T1 - Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds

AU - Taimanov, I. A.

N1 - This work was supported by the Russian Science Foundation under grant no. 24-11-00281, https://rscf.ru/en/project/24-11-00281/.

PY - 2024/12

Y1 - 2024/12

N2 - We describe the relations between Euler’s equations on central extensions of Lie algebras and Euler’s equations on the original algebras that we extend. We consider a special infinite sequence of central extensions of nilpotent Lie algebras constructed from the Lie algebra of formal vector fields on the line, and describe the orbits of coadjoint representations for these algebras. By using the compact nilmanifolds constructed from these algebras by I. K. Babenko and the author, we show that the covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.

AB - We describe the relations between Euler’s equations on central extensions of Lie algebras and Euler’s equations on the original algebras that we extend. We consider a special infinite sequence of central extensions of nilpotent Lie algebras constructed from the Lie algebra of formal vector fields on the line, and describe the orbits of coadjoint representations for these algebras. By using the compact nilmanifolds constructed from these algebras by I. K. Babenko and the author, we show that the covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.

KW - Euler equations on Lie algebras

KW - central extensions of Lie algebras

KW - geodesic flows

KW - magnetic geodesic flows

KW - orbits of coadjoint representations of nilpotent Lie groups

KW - symplectic nilmanifolds

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001512985&origin=inward&txGid=2bd427e5abbceb5b7e5d91ef10be4927

UR - https://www.mendeley.com/catalogue/8abd2e46-c65a-3c56-9f43-90ad3f6436f5/

U2 - 10.1134/S0081543824060221

DO - 10.1134/S0081543824060221

M3 - Article

VL - 327

SP - 300

EP - 312

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 65163425