Towards Kac - van de Leur conjecture: locality of superconformal algebras

TL;DR

This paper proves the locality property of superconformal algebras and introduces quasi-Poisson algebras as a new tool to construct all known simple superconformal algebras.

Contribution

It establishes the locality of superconformal algebras and introduces quasi-Poisson algebras for their construction, advancing understanding of their structure.

Findings

Proved locality of superconformal algebras

Introduced quasi-Poisson algebras

Constructed all known simple superconformal algebras

Abstract

We prove locality of superconformal algebras: every pluperfect superconformal algebra is spanned by coefficients of a finite family of mutually local distributions. We also introduce quasi-Poisson algebras and show that they can be used to construct all known simple superconformal algebras.