In this paper, we study a class of infinite simple Lie conformal algebras associated to a class of generalized Block type Lie algebras. The central extensions by a one-dimensional center \(\mathbb {C}\mathfrak {c}\), conformal derivations and free intermediate series modules of this class of Lie conformal algebras are determined. Moreover, we also show that these Lie conformal algebras do not have any non-trivial finite conformal modules. Consequently, these Lie conformal algebras cannot be embedded into gc_N for any positive integer N.

中文翻译：

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关于一类无限简单的李形共形代数

在本文中，我们研究了与一类广义Block型李代数相关的一类无限简单Lie共形代数。确定了此类Lie共形代数的一维中心\（\ mathbb {C} \ mathfrak {c} \）的中心扩展，共形导数和自由中间级数模块。此外，我们还表明，这些李形保角代数不具有任何非平凡的有限形保角模。因此，对于任何正整数N，这些Lie保形代数无法嵌入到g c _N中。