Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three Academic Article uri icon

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.

published proceedings

  • LINEAR ALGEBRA AND ITS APPLICATIONS

altmetric score

  • 0.25

author list (cited authors)

  • Dykema, K. J., & Klep, I.

citation count

  • 7

complete list of authors

  • Dykema, Kenneth J||Klep, Igor

publication date

  • January 2016