Classification of rank two Lie conformal algebras

TL;DR

This paper provides a comprehensive classification of rank two Lie conformal algebras over the complex numbers and analyzes their automorphism groups, advancing the understanding of their algebraic structures.

Contribution

It offers the first complete classification of rank two Lie conformal algebras and characterizes their automorphism groups.

Findings

Complete classification of rank two Lie conformal algebras

Determination of automorphism groups for these algebras

Establishment of isomorphism classes within this category

Abstract

We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.