Geodesic
The asymptotic approach to the description of the center of a relatively free Lie-nilpotent algebra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 83-94

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In this work, we consider asymptotic properties of dimensional functions related to relatively free algebras. A notion of the $\mathrm{T}$-space inclusion measure into a relatively free algebra is introduced. We calculate this measure for the center of the relatively free Lie-nilpotent algebra of index $5$ and for the $\mathrm{T}$-space of this algebra generated by the long commutator $[x_1, x_2, x_3, x_4]$. Both of these measures coincide being equal to $1/2$. This fact allows us to obtain an asymptotic description of the center. Also, a probability-theoretical view of the inclusion measure is proposed. 
@article{FPM_2020_23_3_a6,
     author = {A. V. Grishin},
     title = {The asymptotic approach to the description of the center of a relatively free {Lie-nilpotent} algebra},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {83--94},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a6/}
}
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A. V. Grishin. The asymptotic approach to the description of the center of a relatively free Lie-nilpotent algebra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 83-94. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a6/