Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4
After the classification of simple Lie algebras over a field of characteristic p > 3, the main problem not yet solved in the theory of finite dimensional Lie algebras is the classification of simple Lie algebras over a field of characteristic 2. The first result for this classification problem en...
- Autores:
-
Payares Guevara, Carlos R.
Arias Amaya, Fabián
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10366
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10366
- Palabra clave:
- Simple Lie 2-algebra
Toral rank
Classical type lie algebra
Contragredient lie algebra
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | After the classification of simple Lie algebras over a field of characteristic p > 3, the main problem not yet solved in the theory of finite dimensional Lie algebras is the classification of simple Lie algebras over a field of characteristic 2. The first result for this classification problem ensures that all finite dimensional Lie algebras of absolute toral rank 1 over an algebraically closed field of characteristic 2 are soluble. Describing simple Lie algebras (respectively, Lie 2-algebras) of finite dimension of absolute toral rank (respectively, toral rank) 3 over an algebraically closed field of characteristic 2 is still an open problem. In this paper we show that there are no classical type simple Lie 2-algebras with toral rank odd and furthermore that the simple contragredient Lie 2-algebra G(F4,a) of dimension 34 has toral rank 4. Additionally, we give the Cartan decomposition of G(F4,a). |
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