On the structure of ℕ-graded Vertex Operator Algebras

2013/10/02 by Geoffrey Mason, Mason, Geoffrey, Gaywalee Yamskulna +1
Mathematics · Physics and Astronomy · #17B6 #17B69 #Advanced Topics in Algebra #Affine transformation #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Current algebra #Duality (order theory) #FOS: Mathematics #Jordan algebra #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Operator algebra #Pure mathematics #Quantum Algebra (math.QA) #Vertex (graph theory) #Vertex operator algebra #math.QA #msc:17B6 #msc:17B69

paper · pdf · doi:10.48550/arxiv.1310.0545

published in arXiv (Cornell University) (Cornell University) · 27 pages

arxiv created 2013/10/02 · openalex publication_date 2013/10/02 · arxiv updated 2013/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the algebraic structure of ℕ-graded vertex operator algebras with conformal grading V=⊕_{n≥ 0} V_n and dim V₀≥ 1. We prove several results along the lines that the vertex operators Y(a, z) for a in a Levi factor of the Leibniz algebra V₁ generate an affine Kac-Moody subVOA. If V arises as a shift of a self-dual VOA of CFT-type, we show that V₀ has a `de Rham structure' with many of the properties of the de Rham cohomology of a complex connected manifold equipped with Poincaré duality.

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