Rationality, regularity, and -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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We demonstrate that, for vertex operator algebras of CFT type, -cofiniteness and rationality is equivalent to regularity. For -cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and -cofinite, is -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