On the structure of split regular -Hom-Jordan-Lie superalgebras
In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form L = H [ ] Σ [ ]2= V [ ]; with H ...
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2022-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/47798 |
| Summary: | In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form
L = H
[
]
Σ
[
]2= V
[
]; with H
[
] a graded linear subspace of the graded abelian subalgebra H and any V [ ]; a well-described ideal of L; satisfying [V [ ]; V []] = 0 if [
] ̸= []: Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular -Hom-Jordan-Lie superalgebra.
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| ISSN: | 0037-8712 2175-1188 |