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The growth of varieties generated by upper-triangular matrices algebras

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Abstract

It is shown that if the characteristic of the basic field does not equal two, then there exists no variety of associative algebras whose growth is intermediate between polynomial and exponential. Let UT s be the algebra of upper triangular matrices of order s over an arbitrary field. V. M. Petrogradsky proved that the exponent of any subvariety of var(UT s ) exists and is an integer number. In his paper the growth estimates for such varieties are reinforced.

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References

  1. V. M. Petrogradsky, “Exponents of subvarieties of upper triangular matrices over arbitrary fields are integral,” Serdika Math., 26, 1001 (2000).

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  2. S. M. Ratseev, “The Growth of some Leibniz Algebras Varieties,” Vestnik Samar. gos. univer., 6(46), 70 (2006) [in Russian].

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  3. S.P. Mishchenko, O. I. Cherevatenko, “Leibniz Algebras Varieties with weak growth,” Vestnik Samar. gos. univer., 9(49), 19 (2006) [in Russian].

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Authors and Affiliations

  1. Faculty of Mathematics and Information Technologies, Ulyanovsk State University, 42 Leo Tolstoy St., Ulyanovsk, 432970, Russia

    S. M. Ratseev

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  1. S. M. Ratseev
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Original Russian Text © S.M. Ratseev, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 66–68

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Ratseev, S.M. The growth of varieties generated by upper-triangular matrices algebras. Moscow Univ. Math. Bull. 66, 50–51 (2011). https://doi.org/10.3103/S0027132211010116

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  • DOI: https://doi.org/10.3103/S0027132211010116

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