Image of arbitrary polynomials on upper triangular matrix algebras

Abstract

The goal of the paper is to give a complete description of the images of noncommutative polynomials with zero constant term on upper triangular matrix algebras over an algebraically closed field. This is a variation of the old and famous Lvov-Kaplansky conjecture.

arXiv admin note: This submission has been withdrawn by arXiv administrators due to withdrawal by the journal. Please see: https://doi.org/10.1016/j.jalgebra.2022.10.038