Abstract
We study the commutator algebras of the homotopes of (−1, 1)-algebras and prove that they are Malcev algebras satisfying the Filippov identity h a (x, y, z) = 0 in the case of strictly (−1, 1)-algebras. We also proved that every Malcev algebra with the identities xy 3 = 0, xy 2 z 2 = 0, and h a (x, y, z) = 0 is nilpotent of index at most 6.
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Original Russian Text Copyright © 2013 Pchelintsev S.V.
The author was supported by the Russian Foundation for Basic Research (Grant 11-01-00938-a) and the Program “Development of the Scientific Potential of Higher School” (Grant 2.1.1.419).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 417–435, March–April, 2013.
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Pchelintsev, S.V. Commutator identities of the homotopes of (−1, 1)-algebras. Sib Math J 54, 325–340 (2013). https://doi.org/10.1134/S0037446613020158
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DOI: https://doi.org/10.1134/S0037446613020158