Neveu-Schwarz and operators algebras I: Vertex operators superalgebras

Abstract

This paper is the first of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we present an elementary, progressive and self-contained approch to vertex operator superalgebra. We then build such a structure from the loop algebra $Lg$ of any simple finite dimensional Lie algebra $g$. The Neveu-Schwarz algebra $Vi{r}_{1/2}$ emerges naturally on. As application, we obtain a unitary action of $Vi{r}_{1/2}$ on the unitary discrete series of $Lg$.

40 pages

References in corpus (4)

• Kac-Moody and Virasoro algebras
• Subfactors and Connes fusion for twisted loop groups
• Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion
• Neveu-Schwarz and operators algebras II: Unitary series and characters

Cited by in corpus (2)

• Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion
• Neveu-Schwarz and operators algebras II: Unitary series and characters