Biderivations and Commuting Linear Maps on Hom-Lie Algebras

Our purpose is to determine skew-symmetric biderivations Formula: see text and commuting linear maps Formula: see text on a multiplicative Hom-Lie algebra Formula: see text having their ranges in an Formula: see text-module Formula: see text, which are both closely related to Formula: see text, the centroid of Formula: see text on Formula: see text. We give the relationship between biderivations and commuting linear maps on a regular Hom-Lie algebra and those on the related Lie algebra. Under appropriate assumptions, we also prove that every Formula: see text in Formula: see text is of the form Formula: see text for some Formula: see text, and Formula: see text coincides with Formula: see text. Besides, we give the algorithms for describing Formula: see text and Formula: see text.