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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Rationality, regularity, and $C_2$-cofiniteness
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by Toshiyuki Abe, Geoffrey Buhl and Chongying Dong PDF
Trans. Amer. Math. Soc. 356 (2004), 3391-3402 Request permission

Abstract:

We demonstrate that, for vertex operator algebras of CFT type, $C_2$-cofiniteness and rationality is equivalent to regularity. For $C_2$-cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and $C_2$-cofinite, $V_L^+$ is $C_2$-cofinite, and the fusion rules are finite.
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Additional Information
  • Toshiyuki Abe
  • Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan
  • Address at time of publication: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan
  • Email: sm3002at@ecs.cmc.osaka-u-ac.jp, abe@ms.u-tokyo.ac.jp
  • Geoffrey Buhl
  • Affiliation: Department of Mathematics, University of California Santa Cruz, Santa Cruz, California 95064
  • Address at time of publication: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
  • Email: gwbuhl@math.ucsc.edu, gbuhl@math.rutgers.edu
  • Chongying Dong
  • Affiliation: Department of Mathematics, University of California Santa Cruz, Santa Cruz, California 95064
  • MR Author ID: 316207
  • Email: dong@math.ucsc.edu
  • Received by editor(s): May 30, 2002
  • Received by editor(s) in revised form: May 15, 2003
  • Published electronically: December 15, 2003
  • Additional Notes: The first author was supported by JSPS Research Fellowships for Young Scientists.
    The second author was supported by NSF grant DMS-9987656 and a research grant from the Committee on Research, UC Santa Cruz.
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 3391-3402
  • MSC (2000): Primary 17B69
  • DOI: https://doi.org/10.1090/S0002-9947-03-03413-5
  • MathSciNet review: 2052955