Geodesic
On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree~3 or~4
Sbornik. Mathematics, Tome 210 (2019) no. 2, pp. 234-244

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This work is concerned with the concept of a graded subspace of the polylinear part of a relatively free algebra and with the measure of inclusion of such a subspace. Other asymptotic characteristics are also considered. In the case of relatively free algebras with the identity of Lie nilpotency of degree 3 and 4, the measure of inclusion is computed for many subspaces; in particular, for the centre and the $T$-space generated by the commutator this measure is $1/2$. Bibliography: 17 titles.
Keywords: identity of Lie nilpotency, graded subspace, measure of inclusion, rate of growth.
Mots-clés : Frobenius relations 
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     author = {A. V. Grishin},
     title = {On the measure of inclusion in relatively free algebras with the identity of {Lie} nilpotency of degree~3 or~4},
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A. V. Grishin. On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree~3 or~4. Sbornik. Mathematics, Tome 210 (2019) no. 2, pp. 234-244. http://geodesic.mathdoc.fr/item/SM_2019_210_2_a2/