Journal of the Mathematical Society of Japan

A generalization of twisted modules over vertex algebras

Kenichiro TANABE

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For an arbitrary positive integer $T$ we introduce the notion of a $(V,T)$-module over a vertex algebra $V$, which is a generalization of a twisted $V$-module. Under some conditions on $V$, we construct an associative algebra $A^{T}_{m}(V)$ for $m\in(1/T)\mathbb N$ and an $A^{T}_{m}(V)$-$A^{T}_{n}(V)$-bimodule $A^{T}_{n,m}(V)$ for $n,m\in(1/T)\mathbb N$ and we establish a one-to-one correspondence between the set of isomorphism classes of simple left $A^{T}_{0}(V)$-modules and that of simple $(1/T)\mathbb N$-graded $(V,T)$-modules.

Article information

J. Math. Soc. Japan, Volume 67, Number 3 (2015), 1109-1146.

First available in Project Euclid: 5 August 2015

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Zentralblatt MATH identifier

Primary: 17B69: Vertex operators; vertex operator algebras and related structures
Secondary: 17B68: Virasoro and related algebras

vertex algebra twisted module


TANABE, Kenichiro. A generalization of twisted modules over vertex algebras. J. Math. Soc. Japan 67 (2015), no. 3, 1109--1146. doi:10.2969/jmsj/06731109.

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