Research on vertex operator algebras associated with parafermion algebras

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We study parafermion vertex operator algebras, which are subalgebras of integrable representations of affine Lie algebras of type A1. Using singular vectors, we classify the irreducible modules for the parafermion vertex operator algebras. Furthermore, C2-cofiniteness is established. It is proved that the dimension of Zhu's algebra coincides with that of C2 algebra. The orbifold of a lattice vertex operator algebra associated with a square root 2 times an ordinary root lattice of type An by an automorphism of order 3 is studied. We classify the irreducible modules for the orbifold. The rationality and C2-cofiniteness of the orbifold are also established.