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 |
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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 |
| _version_ | 1797634046697668608 |
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| author | Valiollah Khalili |
| author_facet | Valiollah Khalili |
| author_sort | Valiollah Khalili |
| collection | DOAJ |
| description | 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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| first_indexed | 2024-03-11T12:02:17Z |
| format | Article |
| id | doaj.art-09e56951f8fd4c57bf3ae9fe26696b43 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T12:02:17Z |
| publishDate | 2022-12-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-09e56951f8fd4c57bf3ae9fe26696b432023-11-07T20:12:13ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882022-12-014110.5269/bspm.47798On the structure of split regular -Hom-Jordan-Lie superalgebrasValiollah Khalili0Arak UniversityIn 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. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/47798 |
| spellingShingle | Valiollah Khalili On the structure of split regular -Hom-Jordan-Lie superalgebras Boletim da Sociedade Paranaense de Matemática |
| title | On the structure of split regular -Hom-Jordan-Lie superalgebras |
| title_full | On the structure of split regular -Hom-Jordan-Lie superalgebras |
| title_fullStr | On the structure of split regular -Hom-Jordan-Lie superalgebras |
| title_full_unstemmed | On the structure of split regular -Hom-Jordan-Lie superalgebras |
| title_short | On the structure of split regular -Hom-Jordan-Lie superalgebras |
| title_sort | on the structure of split regular hom jordan lie superalgebras |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/47798 |
| work_keys_str_mv | AT valiollahkhalili onthestructureofsplitregularhomjordanliesuperalgebras |