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. 
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     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},
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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/

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[2] E.P. Petrov, “Structure, defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim R^{N}/R^{N+1} = 2$”, Siberian Electronic Mathematical Reports, 14 (2017), 1153–-1187 | MR | Zbl

[3] E.P. Petrov, “On identities of finite-dimensional nilpotent algebras”, Algebra i Logika, 30:5 (1991), 540–556 | DOI | MR | Zbl

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