Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 5, Pages 992–1008
DOI: https://doi.org/10.33048/smzh.2023.64.508
(Mi smj7810)
 

Dual coalgebras of Jacobian $n$-Lie algebras over polynomial rings

V. N. Zhelyabin, P. S. Kolesnikov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: We establish the structure of the dual Lie coalgebra for a Lie algebra of the symplectic Poisson bracket (Jacobian-type Poisson bracket) on the algebra of polynomials in evenly many variables. We show that if the base field has characteristic zero then the $n$-ary dual coalgebra for the Jacobian $n$-Lie algebra consists of the same linear functionals as the dual coalgebra for the commutative polynomial algebra.
Keywords: coalgebra, Poisson bracket, Filippov algebra, Jacobian.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0002
Received: 10.04.2023
Revised: 10.04.2023
Accepted: 16.05.2023
Document Type: Article
UDC: 512.554.7
Language: Russian
Citation: V. N. Zhelyabin, P. S. Kolesnikov, “Dual coalgebras of Jacobian $n$-Lie algebras over polynomial rings”, Sibirsk. Mat. Zh., 64:5 (2023), 992–1008
Citation in format AMSBIB
\Bibitem{ZheKol23}
\by V.~N.~Zhelyabin, P.~S.~Kolesnikov
\paper Dual coalgebras of Jacobian $n$-Lie algebras over polynomial rings
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 5
\pages 992--1008
\mathnet{http://mi.mathnet.ru/smj7810}
\crossref{https://doi.org/10.33048/smzh.2023.64.508}
Linking options:
  • https://www.mathnet.ru/eng/smj7810
  • https://www.mathnet.ru/eng/smj/v64/i5/p992
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024