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Fundam. Prikl. Mat., 2016, Volume 21, Issue 2, Pages 217–242 (Mi fpm1727)  

Numerical characteristics of varieties of Poisson algebras

S. M. Ratseev

Ulyanovsk State University

Abstract: The paper is a survey of recent results of investigations on varieties of Poisson algebras. We give constructions of varieties of Poisson algebras with extremal properties, we give equivalent conditions for the polynomial codimension growth of a variety of Poisson algebras, we study varieties of Poisson algebras whose ideals of identities contain the identity $\{x,y\}\cdot ż,t\}=0$, and we study an interrelation between such varieties and varieties of Lie algebras.

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English version:
Journal of Mathematical Sciences (New York), 2019, 237:2, 304–322

UDC: 512.572

Citation: S. M. Ratseev, “Numerical characteristics of varieties of Poisson algebras”, Fundam. Prikl. Mat., 21:2 (2016), 217–242; J. Math. Sci., 237:2 (2019), 304–322

Citation in format AMSBIB
\Bibitem{Rat16}
\by S.~M.~Ratseev
\paper Numerical characteristics of varieties of Poisson algebras
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 2
\pages 217--242
\mathnet{http://mi.mathnet.ru/fpm1727}
\transl
\jour J. Math. Sci.
\yr 2019
\vol 237
\issue 2
\pages 304--322
\crossref{https://doi.org/10.1007/s10958-019-4157-1}


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