Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 6, Pages 8–16 (Mi vmumm188)  

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

Mathematics

Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties

S. M. Ratseev

Ulyanovsk State University, Faculty of Mathematics and Information Technologies
Full-text PDF (269 kB) Citations (1)
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Abstract: Let $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ be the sequence of proper codimensions of a variety $\mathbf{V}$ of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ is presented, i.e. the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ of any such variety $\mathbf{V}$ grows as a polynomial of some degree $k$, but the sequence $\{\gamma_n(\mathbf{W})\}_{n\ge1}$ of any proper subvariety $\mathbf{W}$ in $\mathbf{V}$ grows as a polynomial of degree strictly less than $k$.
Key words: Poisson algebra, variety of algebras, growth of a variety.
Received: 27.06.2014
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 6, Pages 224–232
DOI: https://doi.org/10.3103/S0027132216060024
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: S. M. Ratseev, “Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 6, 8–16; Moscow University Mathematics Bulletin, 71:6 (2016), 224–232
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
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