The images of multilinear polynomials on strictly upper triangular matrices

TL;DR

This paper characterizes the images of multilinear polynomials of any degree when applied to strictly upper triangular matrices, providing a comprehensive understanding of their algebraic behavior.

Contribution

It offers a complete description of the images of multilinear polynomials on strictly upper triangular matrices, extending previous results to arbitrary degree.

Findings

Explicit descriptions of polynomial images

Generalization to polynomials of any degree

Enhanced understanding of algebraic structures

Abstract

The purpose of this paper is to describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra.