0000000000787537

AUTHOR

Sergey Mishchenko

showing 2 related works from this author

Some Numerical Invariants of Multilinear Identities

2017

We consider non-necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe most of the results obtained in recent years on two numerical sequences that can be attached to the multilinear identities satisfied by an algebra: the sequence of codimensions and the sequence of colengths.

ColengthsPolynomial Identitypolynomial identityCodimensions
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Nilpotent varieties and metabelian varieties

2022

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.

Settore MAT/02 - AlgebraGeneral MathematicsNilpotent varieties Metabelian varieties
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