The images of Lie polynomials evaluated on matrices

Alexei Kanel-Belov, Sergey Malev, Louis Rowen

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 sk is not a Lie polynomial, for k>2.

Original languageEnglish
Pages (from-to)4801-4808
Number of pages8
JournalCommunications in Algebra
Issue number11
StatePublished - 2 Nov 2017
Externally publishedYes


  • Lie polynomials
  • matrices


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