## Abstract

It is proved that Zhu's algebra for the vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of a certain associative algebra introduced by Smith. Zhu's algebra for the vertex operator algebra associated to any positive-definite even lattice is also calculated and is related to a generalization of Smith's algebra.

Original language | English (US) |
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Pages (from-to) | 532-551 |

Number of pages | 20 |

Journal | Journal of Algebra |

Volume | 196 |

Issue number | 2 |

DOIs | |

State | Published - Oct 15 1997 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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