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.
Mishchenko S.P., Valenti A. (2021). Correspondence between some metabelian varieties and left nilpotent varieties. JOURNAL OF PURE AND APPLIED ALGEBRA, 225(3) [10.1016/j.jpaa.2020.106538].
Correspondence between some metabelian varieties and left nilpotent varieties
Valenti A.
2021-01-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
Correspondence between some metabelian varieties and left nilpotent varieties.pdf
Solo gestori archvio
Tipologia:
Versione Editoriale
Dimensione
259.03 kB
Formato
Adobe PDF
|
259.03 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
MishchenhoValentiJPAA_106538.pdf
Solo gestori archvio
Tipologia:
Post-print
Dimensione
97.12 kB
Formato
Adobe PDF
|
97.12 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.