Lie 2-algebras of toral rank 3
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916283441741824 |
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| author | Benitez, Germán Guevara, Carlos R. Payares Vanegas, Elkin O. Quintero |
| author_facet | Benitez, Germán Guevara, Carlos R. Payares Vanegas, Elkin O. Quintero |
| contents | In this paper we study Lie 2-algebras over an algebraically closed field of characteristic two, which have a triangulable Cartan subalgebra, and derive some general properties of centerless ones. These properties allow us to do an analysis on simple Lie 2-algebras of toral rank three and provide a necessary condition for simplicity. By means of this latter condition we also conclude that simple Lie 2-algebras with a triangulable Cartan subalgebra of toral rank three and of dimension less than or equal to 16 cannot exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lie 2-algebras of toral rank 3 Benitez, Germán Guevara, Carlos R. Payares Vanegas, Elkin O. Quintero Rings and Algebras 17B50, 17B20, 17B22 In this paper we study Lie 2-algebras over an algebraically closed field of characteristic two, which have a triangulable Cartan subalgebra, and derive some general properties of centerless ones. These properties allow us to do an analysis on simple Lie 2-algebras of toral rank three and provide a necessary condition for simplicity. By means of this latter condition we also conclude that simple Lie 2-algebras with a triangulable Cartan subalgebra of toral rank three and of dimension less than or equal to 16 cannot exist. |
| title | Lie 2-algebras of toral rank 3 |
| topic | Rings and Algebras 17B50, 17B20, 17B22 |
| url | https://arxiv.org/abs/2406.07554 |