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Identities of unitary finite-dimensional algebras

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Algebra and Logic Aims and scope

We deal with growth functions of sequences of codimensions of identities in finite-dimensional algebras with unity over a field of characteristic zero. For three-dimensional algebras, it is proved that the codimension sequence grows asymptotically as a n, where a is 1, 2, or 3. For arbitrary finite-dimensional algebras, it is shown that the codimension growth either is polynomial or is not slower than 2n. We give an example of a finite-dimensional algebra with growth rate an with fractional exponent \( a = \frac{3}{{\sqrt[3]{4}}} + 1 \).

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  1. Moscow State University, Moscow, 119992, Russia

    M. V. Zaitsev

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  1. M. V. Zaitsev
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Correspondence to M. V. Zaitsev.

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Supported by RFBR (project No. 09-01-000303a). (M. V. Zaitsev)

Translated from Algebra i Logika, Vol. 50, No. 5, pp. 563–594, September-October, 2011.

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Zaitsev, M.V. Identities of unitary finite-dimensional algebras. Algebra Logic 50, 381–404 (2011). https://doi.org/10.1007/s10469-011-9151-8

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  • DOI: https://doi.org/10.1007/s10469-011-9151-8

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