On C₂-cofiniteness of parafermion vertex operator algebras

2010/05/11 by Dong, Chongying, Wang, Qing · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1005.1709

Abstract

It is proved that the regularity of parafermion vertex operator algebras associated to integrable highest weight modules for affine Kac-Moody algebra A₁⁽¹⁾ implies the C₂-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 C₂-cofinite and has only finitely many irreducible modules. Also, the parafermion vertex operator algebras with level 1 are determined explicitly.

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• A class of vertex operator algebras generated by Virasoro vectors

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