Maps preserving zeros of a polynomial

Details Maps preserving zeros of a polynomial Maps preserving zeros of a polynomial

2012-04-23

arxiv.org/abs/1204.5215v1

Mathematics

Rings and Algebras

11 pages, accepted for publication in Linear Algebra Appl

Scientific paper

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 $\phi:\A\to \A$ 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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