# On a class of infinite simple Lie conformal algebras

## TL;DR

This paper investigates a class of infinite simple Lie conformal algebras linked to generalized Block type Lie algebras, detailing their extensions, derivations, modules, and embedding properties.

## Contribution

It characterizes the structure and modules of these Lie conformal algebras, showing they lack non-trivial finite modules and cannot embed into $gc_N$.

## Key findings

- Determined central extensions and conformal derivations.
- Showed absence of non-trivial finite conformal modules.
- Proved these algebras cannot embed into $gc_N$.

## Abstract

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, 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 $N$.