RT journal article
T1 Abelian subalgebras and ideals of maximal dimension in Poisson algebras
A1 Fernández Ouaridi, Amir
A1 Navarro, R.M.
A1 Towers, D.A.
A2 Matemáticas
K1 Poisson algebra
K1 Lie algebra
K1 abelian subalgebra
K1 abelian ideal
AB 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.
PB Academic Press Inc.
SN 1090-266X
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35874
UL http://hdl.handle.net/10498/35874
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026