On Multilinear Polynomials In Four Variables Evaluated On Matrices

Abstract

Let $K$ be an algebraically closed field of characteristic $0$ and let $M_n(K)$, $n\ge 3$, be the matrix ring over $K$. We will show that the image of any multilinear polynomial in four variables evaluated on $M_n(K)$ contains all matrices of trace $0$.

8 pages

Cited by in corpus (7)

• Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
• Images of multilinear polynomials of degree up to four on upper triangular matrices
• Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three
• The Mesyan Conjecture: a restatement and a correction
• Images of Multilinear Polynomials in the Algebra of Finitary Matrices Contain Trace Zero Matrices
• A new approach to the Lvov-Kaplansky conjecture through gradings
• The L'vov-Kaplansky Conjecture for Polynomials of Degree Three