Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev; Roman Yavich; Roee Shayer

doi:10.1080/00927872.2021.2021221

Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev, Roman Yavich, Roee Shayer

Department of Mathematics

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

6 Scopus citations

Abstract

In this paper, we prove the generalized Kaplansky conjecture for Jordan algebras of the type J_n, in particular for self-adjoint 2 × 2 matrices over (Formula presented.) over (Formula presented.) (Formula presented.) and (Formula presented.) In fact, we prove that the image of multilinear polynomial must be either {0}, (Formula presented.) the space V of pure elements, or J_n.

Original language	English
Pages (from-to)	2840-2845
Number of pages	6
Journal	Communications in Algebra
Volume	50
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2021.2021221
State	Published - 2022

Keywords

Jordan algebra
Lvov–Kaplansky conjecture
non-associative polynomials

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10.1080/00927872.2021.2021221

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KW - Jordan algebra

KW - Lvov–Kaplansky conjecture

KW - non-associative polynomials

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Evaluations of multilinear polynomials on low rank Jordan algebras

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Keywords

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