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An analog of the Amitsur-Levitzki theorem for matrix superalgebras

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Abstract

We construct a polynomial identity of degree 2(nk + n + k) — min{n, k} for the matrix superalgebra M n,k over a field of characteristic zero. The conjecture is formulated that M n,k lacks any identities of lower degree.

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References

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Authors and Affiliations

  1. Ulyanovsk State University, Ulyanovsk, Russia

    L. M. Samoĭlov

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  1. L. M. Samoĭlov
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Correspondence to L. M. Samoĭlov.

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Original Russian Text Copyright © 2010 Samoĭlov L. M.

The author was supported by the Russian Foundation for Basic Research (Grant 07-01-0080-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 620–625, May–June, 2010.

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Samoĭlov, L.M. An analog of the Amitsur-Levitzki theorem for matrix superalgebras. Sib Math J 51, 491–495 (2010). https://doi.org/10.1007/s11202-010-0051-2

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  • DOI: https://doi.org/10.1007/s11202-010-0051-2

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