On the Conformal biderivations and conformal commuting maps on the current Lie Conformal superalgebras

Abstract

Let $L$ be a Lie conformal superalgebra and $A$ be an associative commutative algebra with unity. We define the current Lie conformal superalgebra by the tensor product $L \otimes A.$ We prove every conformal super-biderivation $\varphi_{\lambda }$ on $L$ is of the form of the centroid $Cent(L)$. Moreover, we show that every Lie conformal super-biderivation on $L\otimes A$ also has the same performance as $L$. We also prove that every Lie conformal linear super-commuting map $\varPsi_{\lambda }$ on $L \otimes A$ belongs to $Cent(L \otimes A)$, if the same holds for $L$ as well.