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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 11, Pages 64–72 (Mi ivm9053)  

This article is cited in 2 scientific papers (total in 2 papers)

On minimal Poisson algebras

S. M. Ratseev

Chair of Information Security and Control Theory, Ul'yanovsk State University, 42 L. Tolstoy str., Ul'yanovsk, 432017 Russia
Full-text PDF (198 kB) Citations (2)
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Abstract: We give Poisson algebra constructions on the base of associative algebras and we explore the relationship between the obtained Poisson algebras and original associative algebras. Based on the obtained structures we give two classes of minimal varieties of Poisson algebras of polynomial growth, i.e., the sequence of codimensions of any such a variety grows as a polynomial of some degree $k$, but the sequence of codimensions of any proper subvariety grows as a polynomial of degree strictly less than $k$. Previously the author showed that there are only two varieties of Poisson algebras of almost polynomial growth. In this paper we give a complete description of all subvarieties of these two varieties.
Keywords: Poisson algebra, associative algebra, variety of algebras, growth of a variety.
Received: 26.03.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 11, Pages 54–61
DOI: https://doi.org/10.3103/S1066369X15110067
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: S. M. Ratseev, “On minimal Poisson algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 64–72; Russian Math. (Iz. VUZ), 59:11 (2015), 54–61
Citation in format AMSBIB
\Bibitem{Rat15}
\by S.~M.~Ratseev
\paper On minimal Poisson algebras
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 11
\pages 64--72
\mathnet{http://mi.mathnet.ru/ivm9053}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 11
\pages 54--61
\crossref{https://doi.org/10.3103/S1066369X15110067}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945175004}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:156
    Full-text PDF :42
    References:39
    First page:13
     
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