Enviar artigo por via de e-mail Short $SL_2$-structures on simple Lie algebras
- Autores: Stasenko R.O.1,2
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Afiliações:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Edição: Volume 214, Nº 4 (2023)
- Páginas: 132-180
- Seção: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133522
- DOI: https://doi.org/10.4213/sm9788
- ID: 133522
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Resumo
In Vinberg's works certain non-Abelian gradings of simple Lie algebras were introduced and investigated, namely, short SO3- and SL3-structures. We investigate a different kind of these, short SL2-structures. The main results refer to the one-to-one correspondence between such structures and certain special Jordan algebras.
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Sobre autores
Roman Stasenko
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Autor responsável pela correspondência
Email: theromestasenko@yandex.ru
without scientific degree, no status
Bibliografia
- E. B. Vinberg, “Non-abelian gradings of Lie algebras”, 50th seminar “Sophus Lie”, Banach Center Publ., 113, Polish Acad. Sci. Inst. Math., Warsaw, 2017, 19–38
- E. B. Vinberg, “Short $operatorname{SO}_3$-structures on simple Lie algebras and associated quasielliptic planes”, Lie groups and invariant theory, Amer. Math. Soc. Transl. Ser. 2, 213, Adv. Math. Sci., 56, Amer. Math. Soc., Providence, RI, 2005, 243–270
- A. A. Albert, “A structure theory for Jordan algebras”, Ann. of Math. (2), 48:3 (1947), 546–567
- N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., 39, Amer. Math. Soc., Providence, R.I., 1968, x+453 pp.
- Э. Б. Винберг, В. В. Горбацевич, А. Л. Онищик, “Строение групп и алгебр Ли”, Группы Ли и алгебры Ли – 3, Итоги науки и техн. Сер. Соврем. пробл. мат. Фундам. направления, 41, ВИНИТИ, М., 1990, 5–253
- L. Conlon, “A class of variationally complete representations”, J. Differential Geometry, 7:1-2 (1972), 149–160
- D. I. Panyushev, “The exterior algebra and “spin” of an orthogonal $mathfrak{g}$-module”, Transform. Groups, 6:4 (2001), 371–396
- V. G. Kac, “Some remarks on nilpotent orbits”, J. Algebra, 64:1 (1980), 190–213
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