Frontiers of Mathematics in China >
Parafermion vertex operator algebras
Received date: 29 Oct 2010
Accepted date: 07 Apr 2011
Published date: 01 Aug 2011
Copyright
This paper reviews some recent results on the parafermion vertex operator algebra associated to the integrable highest weight module ℒ (k, 0) of positive integer level k for any affine Kac-Moody Lie algebra , where g is a finite dimensional simple Lie algebra. In particular, the generators and the C2-cofiniteness of the parafermion vertex operator algebras are discussed. A proof of the well-known fact that the parafermion vertex operator algebra can be realized as the commutant of a lattice vertex operator algebra in ℒ (k, 0) is also given.
Key words： Parafermion vertex operator algebra; C2-cofinite
Chongying DONG , Qing WANG . Parafermion vertex operator algebras[J]. Frontiers of Mathematics in China, 2011 , 6(4) : 567 -579 . DOI: 10.1007/s11464-011-0138-5
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