Biderivations and commuting linear maps on the current Leibniz algebras

In this paper, we extend the framework of Zhao, Ben Hassine, and Chen [Citation26] from current Lie superalgebras to current Leibniz algebras. We study biderivations and commuting linear maps on the current Leibniz algebra G⊗H, where G is a Leibniz algebra and H is a commutative associative algebra with unity. We show that if every skew-symmetric biderivation of G is induced by its centroid, then the same holds for G⊗H. Moreover, every commuting linear map on G⊗H belongs to Cent(G⊗H) whenever this is true for G. These results provide a Leibniz analogue of known theorems for Lie and Lie superalgebras.