A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8
Let be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of dimension 8. Moreover, a bilinear form corres...
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2022-03-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
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| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/13462 |
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| author | Edi Kurniadi Nurul Gusriani Betty Subartini |
| author_facet | Edi Kurniadi Nurul Gusriani Betty Subartini |
| author_sort | Edi Kurniadi |
| collection | DOAJ |
| description | Let be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of dimension 8. Moreover, a bilinear form corresponding to this Frobenius functional is symplectic. Then the obtained symplectic bilinear form induces the left-symmetric algebra structures on . In other words, the Lie algebra is the left-symmetric algebra. In particular, we give the formulas of its left-symmetric algebra structure explicitely. The left-symmetric algebra structures for case of higher dimension of this Lie algebra type are still an open problem to be investigated. |
| format | Article |
| id | doaj-art-deb26141840449cf9c41dab215895e08 |
| institution | OA Journals |
| issn | 2086-0382 2477-3344 |
| language | English |
| publishDate | 2022-03-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj-art-deb26141840449cf9c41dab215895e082025-08-20T02:13:45ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442022-03-017226728010.18860/ca.v7i2.134626152A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8Edi Kurniadi0Nurul Gusriani1Betty Subartini2Department of Mathematics of FMIPA Universitas PadjadjaranDepartment of Mathematics of FMIPA Universitas PadjadjaranDepartment of Mathematics of FMIPA Universitas PadjadjaranLet be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of dimension 8. Moreover, a bilinear form corresponding to this Frobenius functional is symplectic. Then the obtained symplectic bilinear form induces the left-symmetric algebra structures on . In other words, the Lie algebra is the left-symmetric algebra. In particular, we give the formulas of its left-symmetric algebra structure explicitely. The left-symmetric algebra structures for case of higher dimension of this Lie algebra type are still an open problem to be investigated.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/13462left-symmetric algebrafrobenius lie algebrafrobenius functionalsemi-direct sumsymplectic form. |
| spellingShingle | Edi Kurniadi Nurul Gusriani Betty Subartini A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 Cauchy: Jurnal Matematika Murni dan Aplikasi left-symmetric algebra frobenius lie algebra frobenius functional semi-direct sum symplectic form. |
| title | A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 |
| title_full | A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 |
| title_fullStr | A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 |
| title_full_unstemmed | A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 |
| title_short | A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 |
| title_sort | left symmetric structure on the semi direct sum real frobenius lie algebra of dimension 8 |
| topic | left-symmetric algebra frobenius lie algebra frobenius functional semi-direct sum symplectic form. |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/13462 |
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