Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev; Roman Yavich; Roee Shayer

Evaluations of multilinear polynomials on low rank Jordan algebras

Rings and Algebras 2021-11-02 v2

Authors: Sergey Malev , Roman Yavich , Roee Shayer

Abstract

In this paper we prove the generalized Kaplansky conjecture for the Jordan algebras of the type $J_n$ in particular for self adjoint $2\times 2$ matrices over $\R$ , over $\C$ , $\HH$ and $\Oct$ . In fact, we prove that the image of multilinear polynomial must be either $\{0\}$ , $\mathbb{R}$ , the space of pure elements $V$ , or $J_n$ .

Keywords

jordan algebras multilinear polynomials kaplansky conjecture self-adjoint matrices pure elements

Cite

@article{arxiv.2107.05266,
  title  = {Evaluations of multilinear polynomials on low rank Jordan algebras},
  author = {Sergey Malev and Roman Yavich and Roee Shayer},
  journal= {arXiv preprint arXiv:2107.05266},
  year   = {2021}
}

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