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Varieties of linear algebras of polynomial growth. (Russian. English summary) Zbl 1413.16028
Summary: The paper is survey of results of investigations on varieties of linear algebras of polynomial growth. We give equivalent conditions of the polynomial codimension growth of a variety of associative algebras, Lie algebras, Leibniz algebras, Poisson algebras, Leibniz-Poisson algebras. It is shown that in the study of varieties of linear algebras of polynomial growth varieties of almost polynomial growth play an important role.

MSC:
16R10 \(T\)-ideals, identities, varieties of associative rings and algebras
17A32 Leibniz algebras
17B01 Identities, free Lie (super)algebras
17B63 Poisson algebras
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