Correspondence between some metabelian varieties and left nilpotent varieties

Angela Valenti, Sergey Mishchenko

Risultato della ricerca: Articlepeer review

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.
Lingua originaleEnglish
Numero di pagine9
RivistaJournal of Pure and Applied Algebra
Volume225
Stato di pubblicazionePublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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