The images of Lie polynomials evaluated on matrices

Alexei Kanel-Belov; Sergey Malev; Louis Rowen

doi:10.1080/00927872.2017.1282959

The images of Lie polynomials evaluated on matrices

Alexei Kanel-Belov, Sergey Malev, Louis Rowen

Research output: Contribution to journal › Article › peer-review

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Abstract

Kaplansky asked about the possible images of a polynomial f in several noncommuting variables. In this paper, we consider the case of f a Lie polynomial. We describe all the possible images of f in M₂(K) and provide an example of f whose image is the set of non-nilpotent trace zero matrices, together with 0. We provide an arithmetic criterion for this case. We also show that the standard polynomial s_k is not a Lie polynomial, for k>2.

Original language	English
Pages (from-to)	4801-4808
Number of pages	8
Journal	Communications in Algebra
Volume	45
Issue number	11
DOIs	https://doi.org/10.1080/00927872.2017.1282959
State	Published - 2 Nov 2017
Externally published	Yes

Keywords

Lie polynomials
matrices

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10.1080/00927872.2017.1282959

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The images of Lie polynomials evaluated on matrices

Abstract

Keywords

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