Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev; Roman Yavich; Roee Shayer

doi:https://doi.org/10.1080/00927872.2021.2021221

Evaluations of multilinear polynomials on low rank Jordan algebras

Sergey Malev, Roman Yavich, Roee Shayer

Ariel University

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

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

https://doi.org/10.1080/00927872.2021.2021221

Cite this

@article{369e68a969a5488c926642c85938893c,

title = "Evaluations of multilinear polynomials on low rank Jordan algebras",

abstract = "In this paper, we prove the generalized Kaplansky conjecture for Jordan algebras of the type Jn, 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 Jn.",

keywords = "Jordan algebra, Lvov–Kaplansky conjecture, non-associative polynomials",

author = "Sergey Malev and Roman Yavich and Roee Shayer",

note = "Publisher Copyright: {\textcopyright} 2021 Taylor & Francis Group, LLC.",

year = "2022",

doi = "https://doi.org/10.1080/00927872.2021.2021221",

language = "الإنجليزيّة",

volume = "50",

pages = "2840--2845",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "7",

}

TY - JOUR

T1 - Evaluations of multilinear polynomials on low rank Jordan algebras

AU - Malev, Sergey

AU - Yavich, Roman

AU - Shayer, Roee

PY - 2022

Y1 - 2022

N2 - In this paper, we prove the generalized Kaplansky conjecture for Jordan algebras of the type Jn, 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 Jn.

AB - In this paper, we prove the generalized Kaplansky conjecture for Jordan algebras of the type Jn, 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 Jn.

KW - Jordan algebra

KW - Lvov–Kaplansky conjecture

KW - non-associative polynomials

UR - http://www.scopus.com/inward/record.url?scp=85120762595&partnerID=8YFLogxK

U2 - https://doi.org/10.1080/00927872.2021.2021221

DO - https://doi.org/10.1080/00927872.2021.2021221

M3 - مقالة

SN - 0092-7872

VL - 50

SP - 2840

EP - 2845

JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

Evaluations of multilinear polynomials on low rank Jordan algebras

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this