TY - JOUR
T1 - Evaluations of multilinear polynomials on low rank Jordan algebras
AU - Malev, Sergey
AU - Yavich, Roman
AU - Shayer, Roee
N1 - Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.
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 - 10.1080/00927872.2021.2021221
DO - 10.1080/00927872.2021.2021221
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AN - SCOPUS:85120762595
SN - 0092-7872
VL - 50
SP - 2840
EP - 2845
JO - Communications in Algebra
JF - Communications in Algebra
IS - 7
ER -