Abstract
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.
Citation
Kenichiro TANABE. "A generalization of twisted modules over vertex algebras." J. Math. Soc. Japan 67 (3) 1109 - 1146, July, 2015. https://doi.org/10.2969/jmsj/06731109