The Structure of Parafermion Vertex Operator Algebras: General Case

Abstract

Abstract:The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.

Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

“…Next we review the definition of parafermion VOAs and some of the basic properties [10,19]. Definition 3.2.…”

On C2-cofiniteness of parafermion vertex operator algebras

“…In particular, a set of generators for general parafermion vertex operator algebra K (g, k) is obtained. It is also shown that K (g, k) is generated by K (sl 2 , k α ) for positive roots α, where k α ∈ {k, 2k, 3k} is determined by the squared length of α [11]. This suggests that the structure and representation theory for general parafermion vertex operator algebra K (g, k) can be understood by using the structure and representation theory of K (sl 2 , k α ) (see [11] for the details).…”

“…In Section 2, we fix the setting, recall the definition of parafermion vertex operator algebra K (g, k), and present some results on parafermion vertex operator algebra K (g, k) from [3][4][5]11]. In Section 3, we define locally regular vertex operator algebra and prove that any locally regular vertex operator algebra is C 2 -cofinite.…”

“…Although the generators of general parafermion vertex operator algebra K (g, k) are determined in [11], it is far from over to understand the structure theory for K (g, k) completely. The main challenging is to figure out how the generators act on each other or how the generators are related.…”

“…Some aspects of both the structure and representation theory of parafermion vertex operator algebras have been studied in [3][4][5]11]. In particular, a set of generators for general parafermion vertex operator algebra K (g, k) is obtained.…”