Geodesic
Defining relations and identities of finite-generated nilpotent algebra $R$ with condition $\dim R^{N}/R^{N+1} = 2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1048-1064

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In this paper we describe defining relations of $s$-generated nilpotent algebra $R$ over arbitrary field with condition $\dim R^{N}/R^{N+1} = 2$ for some natural number $N \geq 3$. It is proved that such algebra $R$ over a field of characteristic not two satisfies the standard identity of degree $N+2$ if $s\geq N$, or the standard identity of smaller degree than $N$ if $s N$.
Keywords: defining relations, identities, nilpotent algebra. 
@article{SEMR_2018_15_a25,
     author = {E. P. Petrov},
     title = {Defining relations and identities of finite-generated nilpotent algebra $R$ with condition $\dim R^{N}/R^{N+1} = 2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1048--1064},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a25/}
}
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E. P. Petrov. Defining relations and identities of finite-generated nilpotent algebra $R$ with condition $\dim R^{N}/R^{N+1} = 2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1048-1064. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a25/