CONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS



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Abstract

This paper is devoted to the varieties of Leibnitz algebras over a field of zero characteristic. All information about the variety in case of zero characteristic of the base field is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with finite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sufficient condition for a finiteness of colength of variety of Leibnitz algebras.

About the authors

A.V. Polovinkina

ФНПЦ ОАО НПО ”Марс”

Author for correspondence.
Email: morenov.sv@ssau.ru

T.V. Skoraya

Ульяновский государственный университет

Email: morenov.sv@ssau.ru

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Copyright (c) 2014 Polovinkina A., Skoraya T.

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