Geodesic
Structure, defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim\, R^{N}/R^{N+1} = 2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1153-1187

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In this paper we describe structure and defining relations of $2$-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 much smaller degree than $N$ (for large values of $N$).
Keywords: defining relations, identities, nilpotent algebra. 
@article{SEMR_2017_14_a33,
     author = {E. P. Petrov},
     title = {Structure, defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim\, R^{N}/R^{N+1} = 2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1153--1187},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a33/}
}
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E. P. Petrov. Structure, defining relations and identities of finite-dimensional nilpotent algebra $R$ with condition $dim\, R^{N}/R^{N+1} = 2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1153-1187. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a33/