Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras
Let be an associative algebra over a field F of any characteristic with involution * and let K=skew(A)={a in A|a*=-a} be its corresponding sub-algebra under the Lie product [a,b]=ab-ba for all a,b in A . If for some finite dimensional vector space over F and * is an adjoint involution with a sy...
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| Format: | Article |
| Language: | English |
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College of Computer and Information Technology – University of Wasit, Iraq
2022-06-01
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| Series: | Wasit Journal of Computer and Mathematics Science |
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| Online Access: | https://wjcm.uowasit.edu.iq/index.php/wjcm/article/view/39 |
| _version_ | 1797198951360757760 |
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| author | Falah Saad Kareem Hasan M. Shlaka |
| author_facet | Falah Saad Kareem Hasan M. Shlaka |
| author_sort | Falah Saad Kareem |
| collection | DOAJ |
| description |
Let be an associative algebra over a field F of any characteristic with involution * and let K=skew(A)={a in A|a*=-a} be its corresponding sub-algebra under the Lie product [a,b]=ab-ba for all a,b in A . If for some finite dimensional vector space over F and * is an adjoint involution with a symmetric non-alternating bilinear form on V , then * is said to be orthogonal. In this paper, Jordan-Lie inner ideals of the orthogonal Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every Jordan-Lie inner ideals of the orthogonal Lie algebras is either eKe* or is a type one point space.
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| first_indexed | 2024-03-07T19:03:44Z |
| format | Article |
| id | doaj.art-cc4bcabc0137461b86e211a9792333d0 |
| institution | Directory Open Access Journal |
| issn | 2788-5879 2788-5887 |
| language | English |
| last_indexed | 2024-04-24T07:08:01Z |
| publishDate | 2022-06-01 |
| publisher | College of Computer and Information Technology – University of Wasit, Iraq |
| record_format | Article |
| series | Wasit Journal of Computer and Mathematics Science |
| spelling | doaj.art-cc4bcabc0137461b86e211a9792333d02024-04-21T18:57:38ZengCollege of Computer and Information Technology – University of Wasit, IraqWasit Journal of Computer and Mathematics Science2788-58792788-58872022-06-011210.31185/wjcm.Vol1.Iss2.39Jordan-Lie Inner Ideals of the Orthogonal Lie AlgebrasFalah Saad Kareem0Hasan M. Shlaka1Computer science and Maths, University of Kufa, IraqComputer science and Maths, University of Kufa, Iraq Let be an associative algebra over a field F of any characteristic with involution * and let K=skew(A)={a in A|a*=-a} be its corresponding sub-algebra under the Lie product [a,b]=ab-ba for all a,b in A . If for some finite dimensional vector space over F and * is an adjoint involution with a symmetric non-alternating bilinear form on V , then * is said to be orthogonal. In this paper, Jordan-Lie inner ideals of the orthogonal Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every Jordan-Lie inner ideals of the orthogonal Lie algebras is either eKe* or is a type one point space. https://wjcm.uowasit.edu.iq/index.php/wjcm/article/view/39Jordan-Lie Orthogonal Simple Lie |
| spellingShingle | Falah Saad Kareem Hasan M. Shlaka Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras Wasit Journal of Computer and Mathematics Science Jordan-Lie Orthogonal Simple Lie |
| title | Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras |
| title_full | Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras |
| title_fullStr | Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras |
| title_full_unstemmed | Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras |
| title_short | Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras |
| title_sort | jordan lie inner ideals of the orthogonal lie algebras |
| topic | Jordan-Lie Orthogonal Simple Lie |
| url | https://wjcm.uowasit.edu.iq/index.php/wjcm/article/view/39 |
| work_keys_str_mv | AT falahsaadkareem jordanlieinneridealsoftheorthogonalliealgebras AT hasanmshlaka jordanlieinneridealsoftheorthogonalliealgebras |