Bimodules and $g$-rationality of vertex operator algebras
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- by Chongying Dong and Cuipo Jiang PDF
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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.References
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Additional Information
- Chongying Dong
- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- MR Author ID: 316207
- 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. - © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 4235-4262
- MSC (2000): Primary 17B69
- DOI: https://doi.org/10.1090/S0002-9947-08-04430-9
- MathSciNet review: 2395171