In the present paper, we prove that any finite nontrivial irreducible module over a rank two Lie conformal algebra ℋ is of rank one. We also describe the actions of ℋ 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.

中文翻译：

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二阶李共形代数的有限不可约共形模

在本文中，我们证明了任何有限非平凡不可约模在二阶李共形代数上ℋ是排名第一的。我们还描述了ℋ明确地在其有限不可约模上。此外，我们证明了所有有限李共形代数的有限非平凡不可约模，其半单商是 Virasoro 李共形代数的秩为 1。