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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 567–577
DOI: https://doi.org/10.4213/mzm10252 (Mi mzm10252) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Correlation of Poisson Algebras and Lie Algebras in the Language of Identities

S. M. Ratseev

Ulyanovsk State University
Full-text PDF (486 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm10252
Abstract: In the paper, the varieties of Poisson algebras whose ideals of identities contain the identity $\{x,y\}\cdot\{z,t\}=0$ are studied, and the correlation of these varieties with varieties of Lie algebras is investigated. A variety of Poisson algebras of almost exponential growth is presented. An example of a variety of Poisson algebras with fractional exponent is also given.
Keywords: Poisson algebra, Lie algebra, ideal of identities, variety of algebras, almost exponential growth, Specht variety.
Received: 26.12.2012
Revised: 26.06.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 538–547
DOI: https://doi.org/10.1134/S0001434614090284
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: S. M. Ratseev, “Correlation of Poisson Algebras and Lie Algebras in the Language of Identities”, Mat. Zametki, 96:4 (2014), 567–577; Math. Notes, 96:4 (2014), 538–547
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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