Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three
Academic Article
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
abstract
2016 Elsevier Inc. Given a positive integer d, the KaplanskyLvov conjecture states that the set of values of a multilinear noncommutative polynomial fCx 1 ,,x n on the matrix algebra M d (C) is a vector subspace. In this article the technique of using one-wiggle families of Sylvester's clock-and-shift matrices is championed to establish the conjecture for polynomials f of degree three when d is even or d<17.