Year: 2023
Type: preprint
Abstract: The Fagundes-Mello conjecture asserts that every multilinear polynomial on upper triangular matrix algebras is a vector space, which is an improtant variation of the old and famous Lvov-Kaplansky conjecture. The goal of the paper is to give a description of the images of linear polynomials with zero constant term on the upper triangular matrix algebra under a mild condition on the ground field. As a consequence we improve all results on the Fagundes-Mello conjecture. As another consequence we improve some results by Fagundes and Koshlukov on the images of multilinear graded polynomials on upper triangular matrix algebras.
Source: arXiv (Cornell University)
Authors: Luo, Yingyu, Chen, Qian
Institutions: Changchun Normal University, Shanghai Normal University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4362655677