Loop Virasoro Lie conformal algebra

Abstract

The Lie conformal algebra of loop Virasoro algebra, denoted by \documentclass[12pt]{minimal}\begin{document}$\mathscr {CW}$\end{document}CW, is introduced in this paper. Explicitly, \documentclass[12pt]{minimal}\begin{document}$\mathscr {CW}$\end{document}CW is a Lie conformal algebra with \documentclass[12pt]{minimal}\begin{document}$\mathbb {C}[\partial ]$\end{document}C[∂]-basis \documentclass[12pt]{minimal}\begin{document}$\lbrace L_i\,|\,i\in \mathbb {Z}\rbrace$\end{document}{Li|i∈Z} and λ-brackets [Li λ Lj] = (−∂−2λ)Li+j. Then conformal derivations of \documentclass[12pt]{minimal}\begin{document}$\mathscr {CW}$\end{document}CW are determined. Finally, rank one conformal modules and \documentclass[12pt]{minimal}\begin{document}$\mathbb {Z}$\end{document}Z-graded free intermediate series modules over \documentclass[12pt]{minimal}\begin{document}$\mathscr {CW}$\end{document}CW are classified.