Differential Conformal Superalgebras and their Forms

TL;DR

This paper develops the theory of differential conformal superalgebras, establishing their automorphism groups and classifying their forms using Galois cohomology, advancing the mathematical understanding of conformal superalgebra structures.

Contribution

It introduces the formalism of differential conformal superalgebras and applies it to classify N=2 and N=4 conformal superalgebras via Galois cohomology.

Findings

Defined the automorphism group functor for differential conformal superalgebras

Established descent theory in the conformal setting

Classified forms of N=2 and N=4 conformal superalgebras

Abstract

We introduce the formalism of differential conformal superalgebras, which we show leads to the "correct" automorphism group functor and accompanying descent theory in the conformal setting. As an application, we classify forms of N=2 and N=4 conformal superalgebras by means of Galois cohomology.