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arXiv · 1205.5053

Central polynomials for matrices over finite fields

Matej Brešar·Vesselin Drensky
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Abstract

Let $c(x_1,...,x_d)$ be a multihomogeneous central polynomial for the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of positive characteristic $p$. We show that there exists a multihomogeneous polynomial $c_0(x_1,...,x_d)$ of the same degree and with coefficients in the prime field $F_p$ which is central for the algebra $M_n(F)$ for any (possibly finite) field $F$ of characteristic $p$. The proof is elementary and uses standard combinatorial techniques only.

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Matej Brešar, Vesselin Drensky. 2012-05-22. Central polynomials for matrices over finite fields. https://arxiv.org/abs/1205.5053

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