Geodesic
The Gel'fand--Kirillov dimension of relatively free associative algebras
Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1703-1726

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In this paper the Gel'fand–Kirillov dimension $\operatorname{GKdim}(A)$ is calculated for a relatively free associative algebra $A$ over an arbitrary ground field. This dimension is determined by the complexity type of the algebra $A$ or by the set of semidirect products of matrix algebras over a polynomial ring contained in the variety $\operatorname{Var}(A)$. The proof is comparatively elementary and does not use the local representability of relatively free algebras. 
@article{SM_2004_195_12_a0,
     author = {A. Ya. Belov},
     title = {The {Gel'fand--Kirillov} dimension of relatively free associative algebras},
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     pages = {1703--1726},
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     number = {12},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_12_a0/}
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A. Ya. Belov. The Gel'fand--Kirillov dimension of relatively free associative algebras. Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1703-1726. http://geodesic.mathdoc.fr/item/SM_2004_195_12_a0/