Bimodules and 𝑔-rationality of vertex operator algebras

Dong, Chongying; Jiang, Cuipo

doi:10.1090/S0002-9947-08-04430-9

Bimodules and $g$-rationality of vertex operator algebras
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Trans. Amer. Math. Soc. 360 (2008), 4235-4262 Request permission

Abstract:

This paper studies the twisted representations of vertex operator algebras. Let $V$ be a vertex operator algebra and $g$ an automorphism of $V$ of finite order $T.$ For any $m,n\in \frac {1}{T}\mathbb {Z}_+$, an $A_{g,n}(V)$-$A_{g,m}(V)$-bimodule $A_{g,n,m}(V)$ is constructed. The collection of these bimodules determines any admissible $g$-twisted $V$-module completely. A Verma type admissible $g$-twisted $V$-module is constructed naturally from any $A_{g,m}(V)$-module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra $V$ is $g$-rational if and only if its twisted associative algebra $A_g(V)$ is semisimple and each irreducible admissible $g$-twisted $V$-module is ordinary.

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