The structure of parafermion vertex operator algebras

Abstract

It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k coincides with a certain W-algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.

12 pages

References in corpus (3)

• Coset Realization of Unifying W-Algebras
• W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)
• $W$ Strings and Cohomology in Parafermionic Theories

Cited by in corpus (6)

• Tensor categories for vertex operator superalgebra extensions
• Cosets of affine vertex algebras inside larger structures
• Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions
• On Majorana representations of the group $3^2:2$ of 3C-pure type and the corresponding vertex operator algebras
• The classification of vertex operator algebras of OZ-type generated by Ising vectors of $\sigma$-type