## Abstract

We construct two associative algebras from a vertex operator algebra V and a general automorphism g of V. The first, called a g-twisted zero-mode algebra, is a subquotient of what we call a g-twisted universal enveloping algebra of V. These algebras are generalizations of the corresponding algebras introduced and studied by Frenkel-Zhu and Nagatomo-Tsuchiya in the (untwisted) case that g is the identity. The other is a generalization of the g-twisted version of Zhu’s algebra for suitable g-twisted modules constructed by Dong-Li-Mason when the order of g is finite. We are mainly interested in g-twisted V-modules introduced by the first author in the case that g is of infinite order and does not act on V semisimply. In this case, twisted vertex operators in general involve the logarithm of the variable. We construct functors between categories of suitable modules for these associative algebras and categories of suitable (logarithmic) g-twisted V-modules. Using these functors, we prove that the g-twisted zero-mode algebra and the g-twisted generalization of Zhu’s algebra are in fact isomorphic.

Original language | English (US) |
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Pages (from-to) | 3747-3786 |

Number of pages | 40 |

Journal | Transactions of the American Mathematical Society |

Volume | 371 |

Issue number | 6 |

DOIs | |

State | Published - Mar 15 2019 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics