The images of non-commutative polynomials evaluated on the Quaternion algebra

2019/06/12 by Malev, Sergey
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1906.04973

Abstract

Let p be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set M_n(K) of n by n matrices is a vector space. In this paper we settle the analogous conjecture for a quaternion algebra.

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