Computing Derivations on Nilpotent Quadratic Lie Algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910307929030656 |
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| author | Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge |
| author_facet | Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge |
| contents | Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different techniques to obtain any quadratic Lie algebra whose (solvable) radical ideal is nilpotent. To achieve this, we propose two alternative methods, both involving the use of quotients. In addition to their mathematical description, both approaches introduced in this paper have been computationally implemented and are publicly available to use for generating these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing Derivations on Nilpotent Quadratic Lie Algebras Benito, Pilar Rández-Ibáñez, Javier Roldán-López, Jorge Rings and Algebras 17A45, 17B05, 17B30, 17B40, 17-08, 68W30 Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different techniques to obtain any quadratic Lie algebra whose (solvable) radical ideal is nilpotent. To achieve this, we propose two alternative methods, both involving the use of quotients. In addition to their mathematical description, both approaches introduced in this paper have been computationally implemented and are publicly available to use for generating these algebras. |
| title | Computing Derivations on Nilpotent Quadratic Lie Algebras |
| topic | Rings and Algebras 17A45, 17B05, 17B30, 17B40, 17-08, 68W30 |
| url | https://arxiv.org/abs/2401.14348 |