"Nonlinear Jordan centralizer of strictly upper triangular matrices"

Let ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n×n strictly upper triangular matrices with entries in ℱ, and let f:Nn(ℱ)→Nn(ℱ) be a nonlinear Jordan… Click to show full abstract

Let ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n×n strictly upper triangular matrices with entries in ℱ, and let f:Nn(ℱ)→Nn(ℱ) be a nonlinear Jordan centralizer of Nn(ℱ),that is, a map satisfying that f(XY+YX)=Xf(Y)+f(Y)X, for all X, Y∈Nn(ℱ). We prove that f(X)=λX+η(X) where λ∈ℱ and η is a map from Nn(ℱ) into its center ????(Nn(ℱ)) satisfying that η(XY+YX)=0 for every X,Yin Nn(F).

Keywords: mrow; mrow mrow; jats inline; xlink; math; inline formula

Journal Title: Arab Journal of Mathematical Sciences
Year Published: 2019

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