Central polynomials for matrices over finite fields |
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| Authors: | Matej Bre?ar Vesselin Drensky |
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| Institution: | 1. Department of Mathematics, Faculty of Mathematics and Physics , University of Ljubljana , 1000 Ljubljana, Slovenia;2. Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics , University of Maribor , 2000 Maribor, Slovenia matej.bresar@fmf.uni-lj.si;4. Bulgarian Academy of Sciences , Institute of Mathematics and Informatics , Sofia 1113 , Bulgaria |
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| Abstract: | Let c(x 1,?…?,?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 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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| Keywords: | central polynomials matrix algebras |
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