Work

Non-Global Lie Higher Derivations on Triangular Algebras Without Assuming Unity

Year: 2025

Type: article

Abstract: This work establishes a unified structural theory for non-global Lie higher derivations on triangular algebras T, without assuming the existence of a unit element. The primary contribution is the introduction of extreme non-global Lie higher derivations and the proof that every non-global Lie higher derivation on T admits a unique decomposition into three components: a higher derivation, an extreme non-global Lie higher derivation, and a central map vanishing on all commutators [x,y], where x,y∈T satisfy xy=0. This general framework is then explicitly applied to describe such derivations on two significant classes of algebras: upper triangular matrix algebras over faithful algebras and over semiprime algebras. By encompassing both unital and non-unital cases within a single characterization, the theory developed here not only generalizes numerous earlier results but also substantially expands the scope of the existing research landscape.

Source: Axioms

DOI: 10.3390/axioms14110790

Authors: Xinfeng Liang, Yujiao Sun

Institutions: Anhui University of Science and Technology, Beijing Institute of Technology

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, University Natural Science Research Project of Anhui Province