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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 1, Pages 3–19
DOI: https://doi.org/10.4213/tmf9025 (Mi tmf9025) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods

O. L. Kurnyavkoa, I. V. Shirokovba

a Omsk Institute of Water Transport, Omsk, Russia
b Omsk State Technical University, Omsk, Russia
Full-text PDF (473 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9025
Abstract: We offer a method for constructing invariants of the coadjoint representation of Lie groups that reduces this problem to known problems of linear algebra. This method is based on passing to symplectic coordinates on the coadjoint representation orbits, which play the role of local coordinates on those orbits. The corresponding transition functions are their parametric equations. Eliminating the symplectic coordinates from the transition functions, we can obtain the complete set of invariants. The proposed method allows solving the problem of constructing invariants of the coadjoint representation for Lie groups with an arbitrary dimension and structure.
Keywords: invariant, coadjoint representation, Lie group, Lie algebra, polarization, symplectic coordinate.
Funding agency Grant number
Russian Foundation for Basic Research 14-07-00272
Ministry of Education and Science of the Russian Federation 3107
This research is supported in part by the Russian Foundation for Basic Research (Grant No. 14-07-00272) and the Ministry of Education and Science of the Russian Federation in the framework of the main part of the government task in the field of science (Project No. 3107).
Received: 15.08.2015
Revised: 30.10.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 1, Pages 965–979
DOI: https://doi.org/10.1134/S0040577916070011
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. L. Kurnyavko, I. V. Shirokov, “Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods”, TMF, 188:1 (2016), 3–19; Theoret. and Math. Phys., 188:1 (2016), 965–979
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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