Geodesic
Asymptotics of the Codimensions~$c_n$ in the Algebra $F^{(7)}$
Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 25-32

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The paper studies the additive structure of the algebra $F^{(7)}$, i.e., a relatively free associative countably generated algebra with the identity $[x_1,\dots,x_7]=0$ over an infinite field of characteristic $\ne 2,3$. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions $c_n=\dim F_n^{(7)}$ are obtained, where $F_n^{(7)}$ stands for the subspace of multilinear polynomials of degree $n$ in the algebra $F^{(7)}$.
Keywords: identity of Lie nilpotency of degree $7$, proper polynomial, extended Grassmann algebra, linking relations.
Mots-clés : Hall polynomial, inverse polynomial 
@article{MZM_2018_104_1_a2,
     author = {A. V. Grishin},
     title = {Asymptotics of the {Codimensions~}$c_n$ in the {Algebra} $F^{(7)}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {25--32},
     publisher = {mathdoc},
     volume = {104},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a2/}
}
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A. V. Grishin. Asymptotics of the Codimensions~$c_n$ in the Algebra $F^{(7)}$. Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 25-32. http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a2/