Central polynomials for matrices over finite fields

2012/05/22 by Matej Brešar, Vesselin Drensky, Brešar, Matej +1
Mathematics · #16R10 #16R30 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16R10 #msc:16R30

paper · pdf · doi:10.48550/arxiv.1205.5053

5 pages

arxiv created 2012/05/22 · arxiv updated 2012/05/24

Abstract

Let c(x₁,...,x_d) be a multihomogeneous central polynomial for the n× n matrix algebra M_n(K) over an infinite field K of positive characteristic p. We show that there exists a multihomogeneous polynomial c₀(x₁,...,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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