A new approach to the Lvov-Kaplansky conjecture through gradings
Rings and Algebras
2023-07-10 v1
Abstract
In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or a trace zero polynomial, and we use this approach to present an equivalent statement to the Lvov-Kaplansky conjecture.
Keywords
Cite
@article{arxiv.2210.05653,
title = {A new approach to the Lvov-Kaplansky conjecture through gradings},
author = {Ivan Gonzales Gargate and Thiago Castilho de Mello},
journal= {arXiv preprint arXiv:2210.05653},
year = {2023}
}
Comments
10 pages; comments are welcome