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Developments and Retrospectives in Lie Theory pp 247–274Cite as

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

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Part of the book series: Developments in Mathematics ((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.

Supported by the NSF

Partially supported by a grant from the Simons Foundation (# 207862)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Cruz, CA, 95064, USA

    Geoffrey Mason

  2. Department of Mathematical Sciences, Illinois State University, Normal, IL, 61790, USA

    Gaywalee Yamskulna

Authors
  1. Geoffrey Mason
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  2. Gaywalee Yamskulna
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Corresponding author

Correspondence to Geoffrey Mason .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Santa Cruz, Santa Cruz, California, USA

    Geoffrey Mason

  2. Jacobs University, Bremen, Germany

    Ivan Penkov

  3. Department of Mathematics, University of California, Berkeley, Berkeley, California, USA

    Joseph A. Wolf

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Mason, G., Yamskulna, G. (2014). On the Structure of \(\mathbb{N}\)-Graded Vertex Operator Algebras. In: Mason, G., Penkov, I., Wolf, J. (eds) Developments and Retrospectives in Lie Theory. Developments in Mathematics, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-09804-3_12

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