Advanced Structural Analysis of n-Derivations and n-Automorphisms in Nest Algebras via Exponential Mappings

This paper extends the notions of n-derivations and n-automorphisms from Lie algebras to nest algebras via exponential mappings. We establish necessary and sufficient conditions for triangularity, and examine the preservation of the radical, center, and ideals under these higher-order algebraic transformations. The induced group structures of n-automorphisms are explicitly characterized, including inner and non-abelian components. Several concrete examples demonstrate the applicability and depth of the theoretical findings.