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 Mat. Sb., 2019, Volume 210, Number 2, Pages 75–86 (Mi msb9034)

On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4

A. V. Grishin

Moscow State Pedagogical University, Moscow, Russia

Abstract: 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, Frobenius relations, graded subspace, measure of inclusion, rate of growth.

DOI: https://doi.org/10.4213/sm9034

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English version:
Sbornik: Mathematics, 2019, 210:2, 234–244

Bibliographic databases:

Document Type: Article
UDC: 517.538
MSC: Primary 16R10; Secondary 16R40

Citation: A. V. Grishin, “On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4”, Mat. Sb., 210:2 (2019), 75–86; Sb. Math., 210:2 (2019), 234–244

Citation in format AMSBIB
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