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 with U a linear subspace of a maximal abelian subalgebra H and any a well described (split) ideal of , satisfying 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6568-9-2015,
author = {Mar\'\i a J. Arag\'on Peri\~n\'an and Antonio J. Calder\'on Mart\'\i n},
title = {The structure of split regular Hom-Poisson algebras},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {1-13},
zbl = {06602767},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6568-9-2015}
}
María J. Aragón Periñán; Antonio J. Calderón Martín. The structure of split regular Hom-Poisson algebras. Colloquium Mathematicae, Tome 144 (2016) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6568-9-2015/