Research articles
ScienceAsia 50 (2024):ID 2024033 110 doi:
10.2306/scienceasia15131874.2024.033
Additive ξLie σderivations on triangular algebras
Xiaoqin Zhang^{a}, Xiaofei Qi^{b,*}
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, Email: xiaofeiqisxu@aliyun.com
Received 27 May 2022, Accepted 26 Jan 2024
