Z_k-code vertex operator algebras

摘要

We introduce a simple, self-dual, rational, and C_2-cofinite vertex operator algebra of CFT-type associated with a Z_k-code for k ≥ 2. Our argument is based on the Z_k-symmetry among the simple current modules for the parafermion vertex operator algebra K(sl_2, k). We show that it is naturally realized as the commutant of a certain subalgebra in a lattice vertex operator algebra. Furthermore, we construct all the irreducible modules inside a module for the lattice vertex operator algebra.