Non-additive Lie centralizer of infinite strictly upper triangular matrices
محورهای موضوعی : Linear and multilinear algebra; matrix theory
1 - Department of Mathematics, Centre R\'{e}gional des M\'{e}tiers d'Education et de Formation (CRMEF) Tangier, Morocco
کلید واژه: Lie centralizer, strictly upper triangular matrices, commuting map,
چکیده مقاله :
Let $\mathcal{F}$ be an field of zero characteristic and $N_{\infty}(\mathcal{F})$ be the algebra of infinite strictly upper triangularmatrices 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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