Finite irreducible conformal modules of rank two Lie conformal algebras

Abstract

In the present paper, we prove that any finite nontrivial irreducible module over a rank two Lie conformal algebra [Formula: see text] is of rank one. We also describe the actions of [Formula: see text] on its finite irreducible modules explicitly. Moreover, we show that all finite nontrivial irreducible modules of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie conformal algebra are of rank one.

A class of graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra

“…Inspired by [6], one can obtain that any finite semisimple Lie conformal algebra is free artianian. In [19], some properties of free artianian Lie conformal algebra are investigated. Proof.…”

“…[19], Proposition 3.1) Let A be a free artianian Lie conformal algebra. Then any finite free A-module has a free compositions series.Let M be a free C[∂]-module with a C[∂]-basis {J (a,b) | (a, b) ∈ C×C}.…”