| Popis: |
The purpose of this paper is to introduce the class of split regular BiHom-Poisson color algebras, which can be considered as the natural extension of split regular BiHom-Poisson algebras and of split regular Poisson color algebras. Using the property of connections of roots for this kind of algebras, we prove that such a split regular BiHom-Poisson color algebra LL is of the form L=⊕[α]∈Λ/∼I[α]L={\oplus }_{\left[\alpha ]\in \Lambda \text{/} \sim }{I}_{\left[\alpha ]} with I[α]{I}_{\left[\alpha ]} a well described (graded) ideal of LL, satisfying [I[α],I[β]]+I[α]I[β]=0\left[{I}_{\left[\alpha ]},{I}_{\left[\beta ]}]+{I}_{\left[\alpha ]}{I}_{\left[\beta ]}=0 if [α]≠[β]\left[\alpha ]\ne \left[\beta ]. In particular, a necessary and sufficient condition for the simplicity of this algebra is determined, and it is shown that LL is the direct sum of the family of its simple (graded) ideals. |
