In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈nα with 1<2 and 2<3 instead it was established the existence of a variety of fractional polynomial growth with [Formula presented]. In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.
|Numero di pagine||9|
|Rivista||Journal of Pure and Applied Algebra|
|Stato di pubblicazione||Published - 2021|
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