The aim of this paper was to provide a characterization of nonlinear generalized Lie $ n $-higher derivations for a certain class of triangular algebras. It was shown that, under some mild conditions, each component $ G_r $ of a nonlinear generalized Lie $ n $-higher derivation $ \{G_r\}_{r\in N} $ of the triangular algebra $ \mathcal{U} $ could be expressed as the sum of an additive generalized higher derivation and a nonlinear mapping vanishing on all ($ n-1 $)-th commutators on $ \mathcal{U} $.
Citation: He Yuan, Qian Zhang, Zhendi Gu. Characterizations of generalized Lie $ n $-higher derivations on certain triangular algebras[J]. AIMS Mathematics, 2024, 9(11): 29916-29941. doi: 10.3934/math.20241446
The aim of this paper was to provide a characterization of nonlinear generalized Lie $ n $-higher derivations for a certain class of triangular algebras. It was shown that, under some mild conditions, each component $ G_r $ of a nonlinear generalized Lie $ n $-higher derivation $ \{G_r\}_{r\in N} $ of the triangular algebra $ \mathcal{U} $ could be expressed as the sum of an additive generalized higher derivation and a nonlinear mapping vanishing on all ($ n-1 $)-th commutators on $ \mathcal{U} $.
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