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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Bimodules and $ g$-rationality of vertex operator algebras

Authors: Chongying Dong and Cuipo Jiang
Journal: Trans. Amer. Math. Soc. 360 (2008), 4235-4262
MSC (2000): Primary 17B69
Published electronically: February 27, 2008
MathSciNet review: 2395171
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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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Additional Information

Chongying Dong
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064

Cuipo Jiang
Affiliation: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China

Received by editor(s): August 1, 2006
Published electronically: February 27, 2008
Additional Notes: The first author was supported by NSF grants, China NSF grant 10328102 and a Faculty research grant from the University of California at Santa Cruz.
The second author was supported by China NSF grant 10571119.
Article copyright: © Copyright 2008 American Mathematical Society