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:
-
Arias Amaya, Fabián
Payares Guevara, Carlos Rafael
- Tipo de recurso:
- Article of investigation
- 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/
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Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| title |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| spellingShingle |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 Simple Lie 2-algebra Toral rank Classical type lie algebra Contragredient lie algebra LEMB |
| title_short |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| title_full |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| title_fullStr |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| title_full_unstemmed |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| title_sort |
Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4 |
| dc.creator.fl_str_mv |
Arias Amaya, Fabián Payares Guevara, Carlos Rafael |
| dc.contributor.author.none.fl_str_mv |
Arias Amaya, Fabián Payares Guevara, Carlos Rafael |
| dc.subject.keywords.spa.fl_str_mv |
Simple Lie 2-algebra Toral rank Classical type lie algebra Contragredient lie algebra |
| topic |
Simple Lie 2-algebra Toral rank Classical type lie algebra Contragredient lie algebra LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
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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2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-09-22T21:27:13Z |
| dc.date.available.none.fl_str_mv |
2021-09-22T21:27:13Z |
| dc.date.issued.none.fl_str_mv |
2021-04-29 |
| dc.date.submitted.none.fl_str_mv |
2021-09-08 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Payares Guevara, Carlos R. y Fabián A. Arias Amaya. "Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4" Revista de La Unión Matemática Argentina , vol. 62, no. 1, 29 de abril de 2021, págs. 123-139, https://doi.org/10.33044/revuma.1555. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10366 |
| dc.identifier.doi.none.fl_str_mv |
10.33044/revuma.1555 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Payares Guevara, Carlos R. y Fabián A. Arias Amaya. "Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4" Revista de La Unión Matemática Argentina , vol. 62, no. 1, 29 de abril de 2021, págs. 123-139, https://doi.org/10.33044/revuma.1555. 10.33044/revuma.1555 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/10366 |
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eng |
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eng |
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http://purl.org/coar/access_right/c_abf2 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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17 páginas |
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application/pdf |
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Argentina |
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Cartagena de Indias |
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Revista de la Unión Matemática Argentina, Vol. 62, No. 1, 2021 |
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Universidad Tecnológica de Bolívar |
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Arias Amaya, Fabián713ecd4c-d974-4280-a4cd-5129cdc3e781Payares Guevara, Carlos Rafaelvirtual::3293-1Argentina2021-09-22T21:27:13Z2021-09-22T21:27:13Z2021-04-292021-09-08Payares Guevara, Carlos R. y Fabián A. Arias Amaya. "Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4" Revista de La Unión Matemática Argentina , vol. 62, no. 1, 29 de abril de 2021, págs. 123-139, https://doi.org/10.33044/revuma.1555.https://hdl.handle.net/20.500.12585/1036610.33044/revuma.1555Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarAfter 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).17 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Revista de la Unión Matemática Argentina, Vol. 62, No. 1, 2021Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4Artículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Simple Lie 2-algebraToral rankClassical type lie algebraContragredient lie algebraLEMBCartagena de IndiasA. Grishkov and A. Premet, Simple Lie algebras of absolute toral rank 2 in characteristic 2, Preprint. https://www.ime.usp.br/˜grishkov/papers/asp.pdf.A. Grishkov, On simple Lie algebras over a field of characteristic 2, J. Algebra 363 (2012), 14–18. MR 2925843.S. P. Demuˇskin, Cartan subalgebras of the simple Lie p-algebras Wn and Sn, Sibirsk. Mat. Z. ˇ 11 (1970), 310–325. MR 0262310G. M. D. Hogeweij, Almost-classical Lie algebras. I, II, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 4, 441–452, 453–460. MR 0683531.N. Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers, New York, 1962. MR 0143793.N. Jacobson, Abstract derivation and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), no. 2, 206–224. MR 1501922V. G. Kac, The classification of the simple Lie algebras over a field with non-zero characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 385–408. MR 0276286I. Kaplansky, Linear algebra and geometry. A second course, Allyn and Bacon, Boston, MA, 1969. MR 0249444.G. B. Seligman, On Lie algebras of prime characteristic, Mem. Amer. Math. Soc. 19 (1956). MR 0077876.S. Skryabin, Toral rank one simple Lie algebras of low characteristics, J. Algebra 200 (1998), no. 2, 650–700. MR 1610680R. Steinberg, Automorphisms of classical Lie algebras, Pacific J. Math. 11 (1961), 1119–1129. MR 0143845H. Strade, The absolute toral rank of a Lie algebra, in Lie algebras, Madison 1987, 1–28, Lecture Notes in Math., 1373, Springer, Berlin, 1989. MR 1007321.B. Ju. Ve˘ısfe˘ıler and V. G. Kac, Exponentials in Lie algebras of characteristic p, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 762–788. 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