The images of multilinear and semihomogeneous polynomials on the algebra of octonions
The images of multilinear and semihomogeneous polynomials on the algebra of octonions
AbstractThe 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 O over a field F satisfying certain specified conditions (in particular, we prove it for …