The Waring Problem for Matrix Algebras, II

2023/02/10 by Matej Brešar, Brešar, Matej, Peter Šemrl +1
Mathematics · Engineering · #Advanced Topics in Algebra #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.05106

Abstract

Let f bea noncommutativepolynomial of degree m≥ 1 over an algebraically closed field F of characteristic 0. If n≥ m-1 and α₁,α₂,α₃ are nonzero elements from F such that α₁+α₂+α₃=0, then every trace zero n× n matrix over F can be written as α₁ A₁+α₂A₂+α₃A₃ for some A_i in the image of f in M_n(F).

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