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.References
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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