Open AccessCONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS
Author(s) -
А.В. Половинкина,
T. V. Skoraya
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-84-90
Subject(s) - variety (cybernetics) , mathematics , multilinear map , pure mathematics , lie algebra , algebra over a field , zero (linguistics) , philosophy , linguistics , statistics
This paper is devoted to the varieties of Leibnitz algebras over a eld of zero characteristic. All information about the variety in case of zero characteristic of the base eld 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 nite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sucient condition for a niteness of colength of variety of Leibnitz algebras.