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arXiv · 2302.05106

The Waring Problem for Matrix Algebras, II

Matej Brešar·Peter Šemrl
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Abstract

Let $f$ bea noncommutativepolynomial 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 $M_n(F)$.

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Matej Brešar, Peter Šemrl. 2023-02-10. The Waring Problem for Matrix Algebras, II. https://arxiv.org/abs/2302.05106

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