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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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