Correspondence between some metabelian varieties and left nilpotent varieties
- Autori: Mishchenko S.P.; Valenti A.
- Anno di pubblicazione: 2021
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/462059
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.