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Central polynomials and growth functions

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Abstract

The growth of central polynomials for the algebra of n × n matrices in characterstic zero was studied by Regev in [13]. Here we study the growth of central polynomials for any finite-dimensional algebra over a field of characteristic zero. For such an algebra A we prove the existence of two limits called the central exponent and the proper central exponent of A. They give a measure of the exponential growth of the central polynomials and the proper central polynomials of A. We study the range of such limits and we compare them with the PI-exponent of the algebra.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Antonio Giambruno

  2. Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russia

    Mikhail Zaicev

Authors
  1. Antonio Giambruno
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  2. Mikhail Zaicev
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Corresponding author

Correspondence to Antonio Giambruno.

Additional information

The first author was partially supported by the GNSAGA of INDAM.

The second author was supported by the Russian Science Foundation, grant 16-11-10013.

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Giambruno, A., Zaicev, M. Central polynomials and growth functions. Isr. J. Math. 226, 15–28 (2018). https://doi.org/10.1007/s11856-018-1704-2

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  • DOI: https://doi.org/10.1007/s11856-018-1704-2

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