Image of arbitrary polynomials on upper triangular matrix algebras

TL;DR

This paper characterizes the images of noncommutative polynomials with zero constant term on upper triangular matrix algebras, advancing understanding of polynomial mappings in noncommutative algebra.

Contribution

It provides a complete description of polynomial images on upper triangular matrix algebras, addressing a variation of the Lvov-Kaplansky conjecture.

Findings

Describes the image of noncommutative polynomials with zero constant term.

Advances the understanding of polynomial mappings in noncommutative algebra.

Addresses a variation of the Lvov-Kaplansky conjecture.

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.