The structure of split regular Hom-Poisson algebras
Tom 145 / 2016
Streszczenie
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 {\mathfrak P}=U + \sum _{j}{I}_{j} with U a linear subspace of a maximal abelian subalgebra H and any {I}_{j} a well described (split) ideal of {\mathfrak P}, satisfying \{{ I}_j , { I}_k\}+{ I}_j { I}_k=0 if j\not =k. Under certain conditions, the simplicity of {\mathfrak P} is characterized, and it is shown that {\mathfrak P} is the direct sum of the family of its simple ideals.
