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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 1, Pages 241–244 (Mi timm1276)  

Codimensions of varieties of Poisson algebras with Lie nilpotent commutants

S. M. Ratseeva, O. I. Cherevatenkob

a Ulyanovsk State University, Faculty of Mathematics and Information Technologies
b Ul'yanovsk State Pedagogical University

Abstract: We study varieties of Poisson algebras defined by the identities $\{x_1,x_2\}\cdot\{x_3,x_4\}=0$ and $\{\{x_1,x_2\},\ldots,\{x_{2s+1}, x_{2s+2}\}\}=0$, $s\geq 1$. For each of the varieties we find a carrier algebra and build a basis of the $n$th proper polylinear space. We derive exact formulas for exponential generating functions for sequences of codimensions and proper codimensions as well as exact formulas for codimensions and proper codimensions.

Keywords: Poisson algebra, variety of algebras, growth of a variety.

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Bibliographic databases:
UDC: 512.572
Received: 17.01.2015

Citation: S. M. Ratseev, O. I. Cherevatenko, “Codimensions of varieties of Poisson algebras with Lie nilpotent commutants”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 241–244

Citation in format AMSBIB
\Bibitem{RatChe16}
\by S.~M.~Ratseev, O.~I.~Cherevatenko
\paper Codimensions of varieties of Poisson algebras with Lie nilpotent commutants
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 241--244
\mathnet{http://mi.mathnet.ru/timm1276}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497200}
\elib{http://elibrary.ru/item.asp?id=25655613}


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