RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2016, Volume 188, Number 1, Pages 3–19 (Mi tmf9025)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).


DOI: https://doi.org/10.4213/tmf9025

Full text: PDF file (473 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2016, 188:1, 965–979

Bibliographic databases:

Received: 15.08.2015
Revised: 30.10.2015

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
\Bibitem{KurShi16}
\by O.~L.~Kurnyavko, I.~V.~Shirokov
\paper Construction of invariants of the~coadjoint representation of Lie groups using linear algebra methods
\jour TMF
\yr 2016
\vol 188
\issue 1
\pages 3--19
\mathnet{http://mi.mathnet.ru/tmf9025}
\crossref{https://doi.org/10.4213/tmf9025}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3535397}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...188..965K}
\elib{http://elibrary.ru/item.asp?id=26414448}
\transl
\jour Theoret. and Math. Phys.
\yr 2016
\vol 188
\issue 1
\pages 965--979
\crossref{https://doi.org/10.1134/S0040577916070011}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380653700001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84980534442}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9025
  • https://doi.org/10.4213/tmf9025
  • http://mi.mathnet.ru/eng/tmf/v188/i1/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. M. Gracia-Bondia, F. Lizzi, J. C. Varilly, P. Vitale, “The Kirillov picture for the Wigner particle”, J. Phys. A-Math. Theor., 51:25 (2018), 255203  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:227
    Full text:19
    References:26
    First page:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020