The L'vov-Kaplansky Conjecture for Polynomials of Degree Three
Abstract
The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial f in the matrix algebra Mn(K) is a vector space for every n ∈ N. We prove this conjecture for the case where f has degree 3 and K is an algebraically closed field of characteristic 0.
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