On C_2-cofiniteness of parafermion vertex operator algebras

Details On C_2-cofiniteness of parafermion vertex operator algebras On C_2-cofiniteness of parafermion vertex operator algebras

2010-05-11

arxiv.org/abs/1005.1709v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

It is proved that the regularity of parafermion vertex operator algebras associated to integrable highest weight modules for affine Kac-Moody algebra A_1^{(1)} implies the C_2-cofiniteness of parafermion vertex operator algebras associated to integrable highest weight modules for any affine Kac-Moody algebra. In particular, the parafermion vertex operator algebra associated to an integrable highest weight module of small level for any affine Kac-Moody algebra is C_2-cofinite and has only finitely many irreducible modules. Also, the parafermion vertex operator algebras with level 1 are determined explicitly.

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