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The Level One Zhu Algebra for the Heisenberg Vertex Operator Algebra

  • Katrina BarronEmail author
  • Nathan Vander Werf
  • Jinwei Yang
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 37)

Abstract

The level one Zhu algebra for the Heisenberg vertex operator algebra is calculated, and implications for the use of Zhu algebras of higher level for vertex operator algebras are discussed. In particular, we show the Heisenberg vertex operator algebra gives an example of when the level one Zhu algebra, and in fact all its higher level Zhu algebras, do not provide new indecomposable non simple modules for the vertex operator algebra beyond those detected by the level zero Zhu algebra.

Keywords

Vertex operator algebra Heisenberg algebra Conformal field theory 

Notes

Acknowledgements

The authors thank Darlayne Addabbo and Kiyo Nagatomo for reading a draft of this paper and making comments, suggestions, and corrections. The first author is the recipient of a Simons Foundation Collaboration Grant 282095, and greatly appreciates their support.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Katrina Barron
    • 1
    Email author
  • Nathan Vander Werf
    • 2
  • Jinwei Yang
    • 3
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of Mathematics and StatisticsUniversity of NebraskaKearneyUSA
  3. 3.Department of MathematicsUniversity of AlbertaEdmontonCanada

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