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The Waring problem for matrix algebras, IIMatej Brešar,
Peter Šemrl, 2023, original scientific article
Abstract: Let $f$ be a noncommutative polynomial of degree $m\ge 1$ over an algebraically closed field $F$ of characteristic $0$. If $n\ge m-1$ and $\alpha_1,\alpha_2,\alpha_3$ are nonzero elements from $F$ such that $\alpha_1+\alpha_2+\alpha_3=0$, then every trace zero $n\times n$ matrix over $F$ can be written as $\alpha_1 A_1+\alpha_2A_2+\alpha_3A_3$ for some $A_i$ in the image of $f$ in $M_n(F)$.
Keywords: Waring problem, noncommutatative polynomials, matrix algebras
Published in DiRROS: 10.04.2024; Views: 65; Downloads: 29
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