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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quantum dimensions and quantum Galois theory
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by Chongying Dong, Xiangyu Jiao and Feng Xu PDF
Trans. Amer. Math. Soc. 365 (2013), 6441-6469 Request permission

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
  • MR Author ID: 316207
  • Xiangyu Jiao
  • Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
  • MR Author ID: 1036937
  • Feng Xu
  • Affiliation: Department of Mathematics, University of California, Riverside, California 92521
  • MR Author ID: 358033
  • 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.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6441-6469
  • MSC (2010): Primary 17B69
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05863-1
  • MathSciNet review: 3105758