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Isotopes of the alternative monster and the Skosyrsky algebra

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Abstract

We prove that the isotopes of the alternative monster and the Skosyrsky algebra satisfy the identity П 4 i=1 [x i , y i ] = 0. Hence, the algebras themselves satisfy the identity П 4 i=1 (c, x i , y i ) = 0. We also show that none of the identities П n i=1 (c, x i , y i ) = 0 holds in all commutative alternative nil-algebras of index 3. Thus, we refute the Grishkov–Shestakov hypothesis about the structure of the free finitely generated commutative alternative nil-algebras of index 3.

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Authors and Affiliations

  1. Financial University Under the Government of the Russian Federation, Moscow, Russia

    S. V. Pchelintsev

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  1. S. V. Pchelintsev
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Correspondence to S. V. Pchelintsev.

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Original Russian Text Copyright © 2016 Pchelintsev S.V.

Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 850–865, July–August, 2016; DOI: 10.17377/smzh.2016.57.409. Original article submitted September 15, 2015.

The author was supported by the Russian Science Foundation (Grant 14–21–00065).

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Pchelintsev, S.V. Isotopes of the alternative monster and the Skosyrsky algebra. Sib Math J 57, 666–678 (2016). https://doi.org/10.1134/S0037446616040091

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  • DOI: https://doi.org/10.1134/S0037446616040091

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