# Solvability of Poisson algebras

@article{Siciliano2020SolvabilityOP,
title={Solvability of Poisson algebras},
author={Salvatore Siciliano and Hamid Usefi},
journal={arXiv: Rings and Algebras},
year={2020}
}
• Published 5 June 2020
• Mathematics
• arXiv: Rings and Algebras
4 Citations
Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras
• Mathematics
• 2020
In this paper, we first study properties of the lower central chains for Novikov algebras. Then we show that for every Lie nilpotent Novikov algebra~$\mathcal{N}$, the ideal of~$\mathcal{N}$
On a conjecture about solvability of symmetric Poisson algebras
• Mathematics
Bulletin of the London Mathematical Society
• 2021
For a Lie algebra L , let S(L) denote the symmetric Poisson algebra and s(L) the truncated symmetric Poisson algebra of L . In characteristic p≠2 , the conditions under which these Poisson algebras
Products of commutator ideals of some Lie-admissible algebras
• Mathematics
• 2022
. In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More precisely, we ﬁrst
Scale for codimension growth of Poisson PI-algebras
A.Regev proved that the codimension growth of an associative PI-algebra is at most exponential. The author established a scale for the codimension growth of Lie PI-algebras, which includes a series

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Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has
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We study Poisson algebras satisfying polynomial identities. In particular, such algebras satisfy "customary"' identities (Farkas, 1998, 1999) Our main result is that the growth of the corresponding
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• 2006
Abstract.Let L be a restricted Lie algebra. The symmetric algebra Sp(L) of the restricted enveloping algebra u(L) has the structure of a Poisson algebra. We give necessary and sufficient conditions