Neveu-Schwarz and operators algebras I: Vertex operators superalgebras

2010/10/01 by Sébastien Palcoux, Palcoux, Sébastien · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.FA #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.1010.0078

40 pages

openalex publication_date 2010/10/01 · arxiv created 2010/10/07 · arxiv updated 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Vir_1/2 emerges naturally on. As application, we obtain a unitary action of Vir_1/2 on the unitary discrete series of Lg.

Citations

• Operator algebras and conformal field theory
• Subfactors and Connes fusion for twisted loop groups
• Fusion of Positive Energy Representations of LSpin(2n)

Cited by

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

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• Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion
• On the unitary structures of vertex operator superalgebras
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