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Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds Full article

Journal Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605
Output data Year: 2024, Volume: 327, Pages: 300-312 Pages count : 13 DOI: 10.1134/S0081543824060221
Tags Euler equations on Lie algebras, geodesic flows, magnetic geodesic flows, central extensions of Lie algebras, orbits of coadjoint representations of nilpotent Lie groups, symplectic nilmanifolds.
Authors Taimanov I.A. 1
Affiliations
1 Novosibirsk State University

Funding (1)

1 Russian Science Foundation 24-11-00281

Abstract: 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.
Cite: Taimanov I.A.
Central Extensions of Lie Algebras, Dynamical Systems, and Symplectic Nilmanifolds
Proceedings of the Steklov Institute of Mathematics. 2024. V.327. P.300-312. DOI: 10.1134/S0081543824060221 WOS Scopus РИНЦ OpenAlex
Original: Тайманов И.А.
Центральные расширения алгебр Ли, динамические системы и симплектические нильмногообразия
Труды Математического института имени В.А. Стеклова. 2024. Т.327. С.317-329. DOI: 10.4213/tm4447 РИНЦ OpenAlex
Dates:
Submitted: Jul 16, 2024
Accepted: Nov 25, 2024
Published print: Apr 1, 2025
Published online: Apr 1, 2025
Identifiers:
Web of science: WOS:001457341300022
Scopus: 2-s2.0-105001512985
Elibrary: 80615984
OpenAlex: W4409045695
Citing: Пока нет цитирований
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