@misc{10498/35874,
year = {2024},
url = {http://hdl.handle.net/10498/35874},
abstract = {This paper studies the abelian subalgebras and ideals of maximal dimension of Poisson algebras P of dimension n. We introduce the invariants α and β for Poisson algebras, which correspond to the dimension of an abelian subalgebra and ideal of maximal dimension, respectively. We prove that these invariants coincide if α(P) = n−1. We characterize the Poisson algebras with α(P) = n − 2 over arbitrary fields. In particular, we characterize Lie algebras L with α(L) = n − 2. We also show that α(P) = n − 2 for nilpotent Poisson algebras implies β(P) = n−2. Finally, we study these invariants for various distinguished Poisson algebras, providing us with several examples and counterexamples.},
publisher = {Academic Press Inc.},
keywords = {Poisson algebra},
keywords = {Lie algebra},
keywords = {abelian subalgebra},
keywords = {abelian ideal},
title = {Abelian subalgebras and ideals of maximal dimension in Poisson algebras},
doi = {10.1016/J.JALGEBRA.2024.07.032},
author = {Fernández Ouaridi, Amir and Navarro, R.M. and Towers, D.A.},
}