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arXiv · 1204.5215

Maps preserving zeros of a polynomial

J. Alaminos·M. Brešar·Š. Špenko·A. R. Villena
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Abstract

Let $\A$ be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps $ϕ:\A\to \A$ that preserve zeros of $f$. Under certain technical restrictions we solve the problem for general polynomials $f$ in the case where $\A=M_n(F)$. We also consider quite general algebras $\A$, but only for specific polynomials $f$.

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J. Alaminos, M. Brešar, Š. Špenko, A. R. Villena. 2012-04-23. Maps preserving zeros of a polynomial. https://arxiv.org/abs/1204.5215

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