Geodesic
On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 764-771

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We prove that the commutator algebra of the $c$‑homotope of a strictly $(-1,1)$-algebra is nilpotent of step $\le5$, i.e., that $\mathrm{ad}_c(x_1)\dots\mathrm{ad}_c(x_5)=0$; this bound is sharp.
Keywords: strictly $(-1,1)$-algebra, commutator algebra, nilpotency step, right alternative algebra.
Mots-clés : $c$-homotope 
@article{MZM_2013_93_5_a10,
     author = {S. V. Pchelintsev},
     title = {On the {Commutator} {Nilpotency} {Step} of {Strictly} $(-1,1)${-Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {764--771},
     publisher = {mathdoc},
     volume = {93},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a10/}
}
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S. V. Pchelintsev. On the Commutator Nilpotency Step of Strictly $(-1,1)$-Algebras. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 764-771. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a10/