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An almost nilpotent variety of exponent 2

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Abstract

We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.

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Authors and Affiliations

  1. Department of Algebra and Geometric Computations, Ulyanovsk State University, Ulyanovsk, 432970, Russia

    S. Mishchenko

  2. Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni di Tecnologie Chimiche, Automatica e Modelli Matematici, Università di Palermo, 90128, Palermo, Italy

    A. Valenti

Authors
  1. S. Mishchenko
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  2. A. Valenti
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Corresponding author

Correspondence to S. Mishchenko.

Additional information

The first author was partially supported by RFBR grant 10-01-00209a.

The second author was supported in part by MIUR of Italy.

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Mishchenko, S., Valenti, A. An almost nilpotent variety of exponent 2. Isr. J. Math. 199, 241–257 (2014). https://doi.org/10.1007/s11856-013-0029-4

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  • DOI: https://doi.org/10.1007/s11856-013-0029-4

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