On split regular BiHom-Poisson color algebras
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 algebra...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/cf55e3f205214f1199be668ff021178d |
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| Sumario: | 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. |
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