The Level One Zhu Algebra for the Heisenberg Vertex Operator Algebra

Katrina Barron, Nathan Vander Werf, Jinwei Yang

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationSpringer INdAM Series
PublisherSpringer
Pages37-64
Number of pages28
DOIs
StatePublished - 2019

Publication series

NameSpringer INdAM Series
Volume37
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Keywords

  • Conformal field theory
  • Heisenberg algebra
  • Vertex operator algebra

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Barron, K., Vander Werf, N., & Yang, J. (2019). The Level One Zhu Algebra for the Heisenberg Vertex Operator Algebra. In Springer INdAM Series (pp. 37-64). (Springer INdAM Series; Vol. 37). Springer. https://doi.org/10.1007/978-3-030-32906-8_3