Abstract
It is proved that the exponents of certain varieties of Leibniz algebras with nilpotent commutator subalgebras exist and are integer.
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References
A. M. Blokh, “On a generalization of the concept of Lie algebra,” Dokl. Akad. Nauk SSSR 165, 471–473 (1965).
Yu. A. Bakhturin, Identities in Lie Algebras (Nauka, Moscow, 1985) [in Russian].
A. Giambruno and M. V. Zaicev, “On codimension growth of finitely generated associative algebras,” Adv. Math. 140(2), 145–155(1998).
M. V. Zaitcev and S. P. Mishchenko, “Example of variety of Lie algebras with fractional exponent,” J. Math. Sci. (N. Y.) 93 (6), 977–982 (1999).
S. P. Mishchenko, “Lower bounds on the dimensions of irreducible representations of symmetric groups and of the exponents of the exponential of varieties of Lie algebras,” Mat. Sb. 187 (1), 83–94 (1996) [Sb. Math. 187 (1), 81–92 (1996)].
S. P. Mishchenko and V. M. Petrogradsky, “Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra,” Comm. Algebra 27 (5), 2223–2230 (1999).
V. M. Petrogradskii, “On the numerical characteristics of subvarieties of three varieties of Lie algebras,” Mat. Sb. 190(6), 111–126 (1999)[Sb. Math. 190 (5–6), 887–902 (1999)].
S. P. Mishchenko, “On varieties of polynomial growth of Lie algebras over a field of characteristic zero,” Mat. Zametki 40 (6), 713–721 (1986).
V. M. Petrogradskii, “Growth of polynilpotent varieties of Lie algebras, and rapidly increasing entire functions,” Mat. Sb. 188 (6), 119–138 (1997) [Sb. Math. 188 (6), 913–931 (1997)].
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Ratseev, S.M. The growth of varieties of Leibniz algebras with nilpotent commutator subalgebra. Math Notes 82, 96–103 (2007). https://doi.org/10.1134/S0001434607070127
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DOI: https://doi.org/10.1134/S0001434607070127