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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2021
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oai:doaj.org-article:cf55e3f205214f1199be668ff021178d2021-12-05T14:10:53ZOn split regular BiHom-Poisson color algebras2391-545510.1515/math-2021-0039https://doaj.org/article/cf55e3f205214f1199be668ff021178d2021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0039https://doaj.org/toc/2391-5455The 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.Tao YalingCao YanDe Gruyterarticlebihom-lie color algebrabihom-poisson algebraroot spaceroot system17b7517a6017b2217b65MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 600-613 (2021) |
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bihom-lie color algebra bihom-poisson algebra root space root system 17b75 17a60 17b22 17b65 Mathematics QA1-939 |
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bihom-lie color algebra bihom-poisson algebra root space root system 17b75 17a60 17b22 17b65 Mathematics QA1-939 Tao Yaling Cao Yan On split regular BiHom-Poisson color algebras |
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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. |
| format |
article |
| author |
Tao Yaling Cao Yan |
| author_facet |
Tao Yaling Cao Yan |
| author_sort |
Tao Yaling |
| title |
On split regular BiHom-Poisson color algebras |
| title_short |
On split regular BiHom-Poisson color algebras |
| title_full |
On split regular BiHom-Poisson color algebras |
| title_fullStr |
On split regular BiHom-Poisson color algebras |
| title_full_unstemmed |
On split regular BiHom-Poisson color algebras |
| title_sort |
on split regular bihom-poisson color algebras |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/cf55e3f205214f1199be668ff021178d |
| work_keys_str_mv |
AT taoyaling onsplitregularbihompoissoncoloralgebras AT caoyan onsplitregularbihompoissoncoloralgebras |
| _version_ |
1718371628947079168 |