Automorphisms and twisted forms of the N = 1, 2, 3 Lie conformal superalgebras

TL;DR

This paper classifies N=1, 2, 3 superconformal Lie algebras using differential non-abelian cohomology, revealing the automorphism structures and providing a new methodological approach.

Contribution

It introduces a novel classification method for superconformal Lie algebras based on differential non-abelian cohomology, emphasizing automorphism groups.

Findings

Classification of N=1, 2, 3 superconformal Lie algebras

Description of automorphism groups of these superalgebras

Introduction of a new cohomological technique for algebra classification

Abstract

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of automorphisms of the corresponding Lie conformal superalgebra is a key ingredient of the proof.