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arXiv · 2210.05653

A new approach to the Lvov-Kaplansky conjecture through gradings

Ivan Gonzales Gargate·Thiago Castilho de Mello
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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.

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Ivan Gonzales Gargate, Thiago Castilho de Mello. 2022-10-11. A new approach to the Lvov-Kaplansky conjecture through gradings. https://doi.org/10.1016/j.laa.2023.06.010

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