It is proved that there exist exactly two almost nilpotent varieties of Leibniz algebras over a field of zero characteristic.
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- Title Almost nilpotent varieties of Leibniz algebras
- Headline Almost nilpotent varieties of Leibniz algebras
- Publesher
Tomsk State University
- Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 2 (28)
- Date:
- DOI
Keywords
алгебра Ли, алгебра Лейбница, почти нильпотентное многообразие, диаграмма Юнга, Leibniz algebra, Lie algebra, almost nilpotent variety, Young diagramAuthors
References
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Giambruno A. and Zaicev M. Polynomial identities and asymptotic methods. American Mathematical Society Providence, RI, 2005. 352 p.
Ширшов А. И. и др. Кольца, близкие к ассоциативным. М.: Наука, 1978. 432 с.
Зельманов Е. И. Об энгелевых алгебрах Ли // ДАН СССР. 1987. Т. 292. №2. С. 265-268.
Drensky V. and Cattaneo G. M. P. Varieties of metabelian Leibniz algebras // J. Algebra Appl. 2002. V. 1. No. 1. P. 31-50.
Череватенко О. И. Некоторые эффекты роста тождеств линейных алгебр: дис.. канд. физ.-мат. наук. Ульяновск, 2008. 69 с.
Фролова Ю. Ю. О нильпотентности энгелевой алгебры Лейбница // Вестник Московского государственного университета. Сер. 1. Математика. Механика. 2011. №3. С. 63-65. REFERENCES
Bakhturin Yu. A. Tozhdestva v algebrakh Li [Identities of Lie Algebras]. Moscow, Nauka Publ., 1985. 448 p. (in Russian)
Giambruno A. and Zaicev M. Polynomial identities and asymptotic methods. American Mathematical Society Providence, RI, 2005. 352 p.
Shirshov A. I. et al. Kol'tsa, blizkie k assotsiativnym [Rings that are Nearly Associative]. Moscow, Nauka Publ., 1978. 432 p. (in Russian)
Zel'manov E. I. Ob engelevykh algebrakh Li [On Engel Lie algebras]. Reports USSR Academy of Sciences, 1987, vol.292, no.2, pp.265-268. (in Russian)
Drensky V. and Cattaneo G.M.P. Varieties of metabelian Leibniz algebras. J. Algebra Appl., 2002, vol.1, no. 1, pp. 31-50.
Cherevatenko O. I. Nekotorye effekty rosta tozhdestv lineynykh algebr [Some Effects of Linear Algebra Identities Increase.] PhD Thesis, Ul'yanovsk, 2008. 69 p. (in Russian)
Frolova Yu. Yu. O nil'potentnosti engelevoy algebry Leybnitsa [On the nilpotency of Engel Leibniz algebra.] MSU Bulletin. Ser. 1. Mathematics. Mechanics. 2011, no.3, pp. 63-65. (in Russian)

Almost nilpotent varieties of Leibniz algebras | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2015. № 2 (28).
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