Loop Virasoro Lie Conformal Algebra

Abstract: The Lie conformal algebra of loop Virasoro algebra, denoted by $\mathscr{CW}$, is introduced in this paper. Explicitly, $\mathscr{CW}$ is a Lie conformal algebra with $\mathbb{C}[\partial]$-basis ${L_i\,|\,i\in\mathbb{C}}$ and $\lambda$-brackets $[L_i\, {}\lambda \, L_j]=(-\partial-2\lambda) L{i+j}$. Then conformal derivations of $\mathscr{CW}$ are determined. Finally, rank one conformal modules and $\mathbb{Z}$-graded free intermediate series modules over $\mathscr{CW}$ are classified.