Abstract
It is proved that the colength of every API-variety of Lie algebras grows polynomially, and we give a number of examples in which the colength grows more rapidly than any polynomial function does. These indicate that for many of the important varieties of Lie algebras, such as varieties of solvable algebras of derived length 3, varieties generated by some infinite-dimensional simple algebras of Cartan type, or by certain Katz-Mudi algebras, the growth of colength will be superpolynomial.
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Additional information
Supported by RFFR grants No. 96-01-00146 and No. 96-15-96050.
Translated fromAlgebra i Logika, Vol. 38, No. 2, pp. 161–175, March–April, 1999.
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Zaitsev, M.V., Mischenko, S.P. The polynomial growth of colength of varieties of Lie algebras. Algebr Logic 38, 84–92 (1999). https://doi.org/10.1007/BF02671722
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DOI: https://doi.org/10.1007/BF02671722