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arXiv · 2107.05266

Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev·Roman Yavich·Roee Shayer
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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 $J_n$.

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Sergey Malev, Roman Yavich, Roee Shayer. 2021-10-30. Evaluations of multilinear polynomials on low rank Jordan algebras. https://arxiv.org/abs/2107.05266

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