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
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.
identity of Lie nilpotency, Frobenius relations, graded subspace, measure of inclusion, rate of growth.
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Sbornik: Mathematics, 2019, 210:2, 234–244
MSC: Primary 16R10; Secondary 16R40
Received: 04.11.2017 and 11.04.2018
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
\paper On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree~3 or~4
\jour Mat. Sb.
\jour Sb. Math.
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