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ScienceAsia 50 (2024):ID 2024033 1-10 |doi: 10.2306/scienceasia1513-1874.2024.033

Additive ξ-Lie σ-derivations on triangular algebras

Xiaoqin Zhanga, Xiaofei Qib,*

ABSTRACT:      Let A and B be unital algebras over a field F, M be a faithful (A ,B)-bimodule, and let U = Tri(A ,M,B) be the triangular algebra. Assume that x0 ? U is some fixed element, ? ? F and ? is an additive automorphism of U . It is shown that, under some mild conditions, if an additive map L : U ? U satisfies L(x y ??y x) = L(x) y ???( y)L(x)+?(x)L( y)??L( y)x for x, y ? U with x y = x0 , then L is an additive ?-derivation if ? 6= 1 and is the sum of an additive ?-derivation and a special central valued additive map if ? = 1; and based on this, all additive ?-Lie ?-derivations for each possible ? on U are characterized completely. All these results generalize some known related ones from different directions.

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a School of Statistics, Shanxi University of Finance and Economics, Taiyuan 030006 China
b School of Mathematical Science, Shanxi University, Taiyuan 030006 China

* Corresponding author, E-mail: xiaofeiqisxu@aliyun.com

Received 27 May 2022, Accepted 26 Jan 2024