The Waring Problem for Matrix Algebras

2021/03/19 by Bresar, Matej, Semrl, Peter · 2 citations
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2103.10708

Abstract

If a noncommutative polynomial f is neither an identity nor a central polynomial of \mathcal A=M_n(\C), then every trace zero matrix in \mathcal A can be written as a sum of two matrices from f(\mathcal A)-f(\mathcal A). Moreover, "two" cannot be replaced by "one".

Cited by

• Dynamics of Word Maps on Groups and Polynomial Maps on Algebras
• On sums and products of diagonalizable matrices over division rings

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