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arXiv · 1508.01238

Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three

Kenneth J. Dykema·Igor Klep
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Abstract

Given a positive integer d, the Kaplansky-Lvov conjecture states that the set of values of a multilinear noncommutative polynomial f 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.

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Kenneth J. Dykema, Igor Klep. 2015-08-05. Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three. https://doi.org/10.1016/j.laa.2016.08.005

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