We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.

Valenti Angela , Mishchenko Sergey (2022). Nilpotent varieties and metabelian varieties. TURKISH JOURNAL OF MATHEMATICS, 46(Special Issue 2), 2023-2033 [10.55730/1300-0098.3250].

Nilpotent varieties and metabelian varieties

Valenti Angela
;
2022-01-01

Abstract

We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.
2022
Settore MAT/02 - Algebra
Valenti Angela , Mishchenko Sergey (2022). Nilpotent varieties and metabelian varieties. TURKISH JOURNAL OF MATHEMATICS, 46(Special Issue 2), 2023-2033 [10.55730/1300-0098.3250].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/579490
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