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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quantum dimensions and quantum Galois theory


Authors: Chongying Dong, Xiangyu Jiao and Feng Xu
Journal: Trans. Amer. Math. Soc. 365 (2013), 6441-6469
MSC (2010): Primary 17B69
Published electronically: August 20, 2013
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Abstract: The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents of a rational vertex operator algebra is given and a full Galois theory for rational vertex operator algebras is established using the quantum dimensions.


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Additional Information

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

Xiangyu Jiao
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064

Feng Xu
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05863-1
PII: S 0002-9947(2013)05863-1
Received by editor(s): January 12, 2012
Received by editor(s) in revised form: April 24, 2012
Published electronically: August 20, 2013
Additional Notes: The first author was supported by NSF grants and a faculty research fund from the University of California at Santa Cruz
The third author was supported by an NSF grant and a faculty research fund from the University of California at Riverside.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.