@article{Alshanqiti2026, 
author = {Omaima Alshanqiti and Ashutosh Pandey and Mani Shankar Pandey},
title = {Generalized derivations and quasi derivations of current    Hom-   Lie algebras},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4872-4889},
keywords = {Hom-Lie algebra, generalized derivations, quasiderivation, centroid},
url = {https://www.sciopen.com/article/10.3934/math.2026199},
doi = {10.3934/math.2026199},
abstract = {In this paper, we investigate the structure of generalized derivations and quasiderivations of the tensor product algebra        H    ⊗      A  , where        H   is a Hom-Lie algebra and        A   is a commutative associative algebra with unity over the field        K  . We examine whether every generalized derivation (respectively, quasiderivation) of        H    ⊗      A   can be expressed as a sum of a derivation and a linear map in the centroid of        H    ⊗      A  , provided that this property holds for        H  . We establish a partial affirmative result under suitable conditions and discuss the algebraic implications of our findings.}
}