# Non-additive Lie centralizer of infinite strictly upper triangular matrices

Document Type: Research Paper

Author

Department of Mathematics‎, ‎Centre R'{e}gional des M'{e}tiers‎ ‎d'Education et de Formation (CRMEF) Tangier‎, ‎Morocco

Abstract

‎Let $\mathcal{F}$ be an field of zero characteristic and $N_{\infty‎}(‎\mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $\mathcal{F}$‎, ‎and $f:N_{\infty}(\mathcal{F}‎)\rightarrow N_{\infty}(\mathcal{F})$ be a non-additive Lie centralizer of $‎N_{\infty }(\mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Y\in N_{\infty}(\mathcal{F})$‎. ‎We prove that $f(X)=\lambda X$‎, ‎where $\lambda \in \mathcal{F}$‎.

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