English

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