The structure of split regular Hom-Poisson algebras

María J. Aragón Periñán, and Antonio J. Calderón Martín. "The structure of split regular Hom-Poisson algebras." Colloquium Mathematicae 145.1 (2016): 1-13. <http://eudml.org/doc/286480>.

@article{MaríaJ2016,
abstract = {We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form $ = U + ∑_\{j\} I_\{j\}$ with U a linear subspace of a maximal abelian subalgebra H and any $I_\{j\}$ a well described (split) ideal of , satisfying $\{I_\{j\},I_\{k\}\} + I_\{j\}I_\{k\} = 0$ if j ≠ k. Under certain conditions, the simplicity of is characterized, and it is shown that is the direct sum of the family of its simple ideals.},
author = {María J. Aragón Periñán, Antonio J. Calderón Martín},
journal = {Colloquium Mathematicae},
keywords = {Hom-algebra; Poisson algebra; root; root space; structure theory},
language = {eng},
number = {1},
pages = {1-13},
title = {The structure of split regular Hom-Poisson algebras},
url = {http://eudml.org/doc/286480},
volume = {145},
year = {2016},
}

TY - JOUR
AU - María J. Aragón Periñán
AU - Antonio J. Calderón Martín
TI - The structure of split regular Hom-Poisson algebras
JO - Colloquium Mathematicae
PY - 2016
VL - 145
IS - 1
SP - 1
EP - 13
AB - We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form $ = U + ∑_{j} I_{j}$ with U a linear subspace of a maximal abelian subalgebra H and any $I_{j}$ a well described (split) ideal of , satisfying ${I_{j},I_{k}} + I_{j}I_{k} = 0$ if j ≠ k. Under certain conditions, the simplicity of is characterized, and it is shown that is the direct sum of the family of its simple ideals.
LA - eng
KW - Hom-algebra; Poisson algebra; root; root space; structure theory
UR - http://eudml.org/doc/286480
ER -