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The Images of Multilinear and Semihomogeneous Polynomials on the Algebra of Octonions by Kanel-Belov, Alexei; Malev, Sergey; Pines, Coby; Rowen, Louis is a scholarly article available to read on EtoBox.

What is The Images of Multilinear and Semihomogeneous Polynomials on the Algebra of Octonions about?

The generalized L'vov-Kaplansky conjecture states that for any finite-dimensional simple algebra $A$ the image of a multilinear polynomial on $A$ is a vector space. In this paper we prove it for the algebra of octonions $\mathbb{O}$ over a field satisfying certain specified conditions (in particular, we prove it for quadratically closed field and for field $\mathbb{R}$). In fact, we prove that the image set must be either $\{0\}$, $F$, the space of pure octonions $V$, or $\mathbb{O}$. We discuss possible evaluations of semihomogeneous polynomials on $\mathbb{O}$ and of arbitrary polynomials on the corresponding Malcev algebra.

Author

Kanel-Belov, Alexei; Malev, Sergey; Pines, Coby; Rowen, Louis

Published

2022

Language

EN