6533b838fe1ef96bd12a3c0b
RESEARCH PRODUCT
Correspondence between some metabelian varieties and left nilpotent varieties
S. MishchenkoA. Valentisubject
Class (set theory)Pure mathematicsAlgebra and Number TheoryAnticommutativityFractional polynomialVarietiesMathematics::Rings and Algebras010102 general mathematicsGrowth01 natural sciencesSettore MAT/02 - AlgebraMathematics::Group TheoryTransfer (group theory)NilpotentCodimension0103 physical sciences010307 mathematical physics0101 mathematicsVariety (universal algebra)Constant (mathematics)Commutative propertyMathematicsdescription
Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-03-01 | Journal of Pure and Applied Algebra |