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In the present paper, we prove that any finite non-trivial irreducible module over a rank two Lie conformal algebra $mathcal{H}$ is of rank one. We also describe the actions of $mathcal{H}$ on its finite irreducible modules explicitly. Moreover, we show that all finite non-trivial irreducible modules of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie conformal algebra are of rank one.
In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $mathbb{Z}^+$-graded Lie conformal algebras $mathcal{L}=bigoplus_{i=0}^{infty
In the present paper, we introduce a class of infinite Lie conformal superalgebras $mathcal{S}(p)$, which are closely related to Lie conformal algebras of extended Block type defined in cite{CHS}. Then all finite non-trivial irreducible conformal mod
In this paper, we introduce a class of infinite Lie conformal algebras $mathfrak{B}(alpha,beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $mathfrak{B}(p)$ and its non-trivial conformal modules of $Z$-graded free intermedi
We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over ${frak {B}
In a previous paper by the authors, we obtain the first example of a finitely freely generated simple $mathbb Z$-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper, we obtain, a