Super-biderivations and linear super-commuting maps on the current Lie superalgebras

In this paper, we define the current Lie superalgebra L circle times A, where L is a Lie superalgebra and A is an associative commutative algebra with unity. we proved every skew-symmetric super-biderivation on L circle times A is of the form of the centroid, if the same holds true for L. We also proved every linear super-commuting map on L circle times A belong to Cent(L circle times A), if the same holds true for L.