Geodesic
Representations of the symmetric group and varieties of linear algebras
Sbornik. Mathematics, Tome 43 (1982) no. 1, pp. 85-101 
V. S. Drenski. Representations of the symmetric group and varieties of linear algebras. Sbornik. Mathematics, Tome 43 (1982) no. 1, pp. 85-101. http://geodesic.mathdoc.fr/item/SM_1982_43_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The representation theory of the symmetric group is used to study varieties of linear algebras over a field of characteristic 0. The relatively free algebras and the lattice of subvarieties of the variety of Lie algebras $\mathfrak{AN}_2\cap\mathfrak N_2\mathfrak A$ are described. An example of an almost finitely based variety of linear algebras if constructed. A continuous set of locally finite varieties forming a chain with respect to inclusion is indicated. Information is obtained on the variety of Lie algebras (resp., associative algebras with 1) generated by the second-order matrix algebra. In particular, distributivity of the lattice of subvarieties is proved, and in the Lie case a relatively free algebra is described. Bibliography: 16 titles.

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