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Transactions of the American Mathematical Society

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

 

 

Rationality, regularity, and $C_2$-cofiniteness


Authors: Toshiyuki Abe, Geoffrey Buhl and Chongying Dong
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3391-3402
MSC (2000): Primary 17B69
DOI: https://doi.org/10.1090/S0002-9947-03-03413-5
Published electronically: December 15, 2003
MathSciNet review: 2052955
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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
Email: dong@math.ucsc.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03413-5
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.
Article copyright: © Copyright 2003 American Mathematical Society