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On the Structure of \(\mathbb{N}\)-Graded Vertex Operator Algebras

  • Geoffrey MasonEmail author
  • Gaywalee Yamskulna
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 38)

Abstract

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

Key words

Vertex operator algebra Lie algebra Leibniz algebra. 

Mathematics Subject Classification (2010):

17B65 17B69. 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA
  2. 2.Department of Mathematical SciencesIllinois State UniversityNormalUSA

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