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

TL;DR

This paper investigates the structure of conformal super-biderivations and commuting maps on current Lie conformal superalgebras, showing they are closely related to the centroid of the algebra.

Contribution

It establishes that conformal super-biderivations and super-commuting maps on current Lie conformal superalgebras are characterized by the centroid, extending known results from the base algebra.

Findings

Conformal super-biderivations on L are of the form of the centroid.

Such biderivations on L ⊗ A behave similarly to those on L.

Super-commuting maps on L ⊗ A belong to the centroid if they do on L.

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.