Loop W(a,b) Lie conformal algebra

Fix [Formula: see text], let [Formula: see text] be the loop [Formula: see text] Lie algebra over [Formula: see text] with basis [Formula: see text] and relations [Formula: see text], where [Formula: see text]. In this paper, a formal distribution Lie algebra of [Formula: see text] is constructed. Then the associated conformal algebra [Formula: see text] is studied, where [Formula: see text] has a [Formula: see text]-basis [Formula: see text] with [Formula: see text]-brackets [Formula: see text] and [Formula: see text]. In particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules.