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Research Article | Open Access

Triangular algebras with nonlinear higher Lie n-derivation by local actions

Xinfeng Liang( ), Mengya Zhang
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China
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Abstract

This paper was devoted to the study of the so-called nonlinear higher Lie n-derivation of triangular algebras T , where n is a nonnegative integer greater than two. Under some mild conditions, we proved that every nonlinear higher Lie n-derivation by local actions on the triangular algebras is of a standard form. As an application, we gave a characterization of higher Lie n-derivation by local actions on upper triangular matrix algebras, block upper triangular matrix algebras and nest algebras, respectively.

Keywords

higher Lie n-derivationhigher derivationslocal actiontriangular algebrasnest algebras
CLC number: 15A78, 16W25, 17B40

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 2549-2583
DOI: 10.3934/math.2024126

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Cite this article:
Liang X, Zhang M. Triangular algebras with nonlinear higher Lie n-derivation by local actions. AIMS Mathematics, 2024, 9(2): 2549-2583. https://doi.org/10.3934/math.2024126

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Received: 14 November 2023
Revised: 07 December 2023
Accepted: 10 December 2023
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)