The L'vov-Kaplansky Conjecture for Polynomials of Degree Three

Abstract

The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial $f$ in the matrix algebra $M_n(K)$ is a vector space for every $n\in \mathbb{N}$. We prove this conjecture for the case where $f$ has degree $3$ and $K$ is an algebraically closed field of characteristic $0$.

24 pages

References in corpus (3)

• Images of multilinear polynomials on $n\times n$ upper triangular matrices over infinite fields
• Multilinear Polynomials Are Surjective on Algebras With Surjective Inner Derivations
• The Mesyan Conjecture: a restatement and a correction