ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

Abstract

The W 3 algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V √ 2A2 associated with a lattice of type √ 2A 2 by using both coset construction and orbifold theory. It is proved that W 3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.

On intertwining operators and finite automorphism groups of vertex operator algebras

“…We recall some properties of W in [3]. W is generated by the Virasoro element ω and an element J of weight 3.…”

“…For an irreducible W-module N , h N denotes the eigenvalue for L(0) on N(0) and k N denotes the eigenvalue for J (0) on N(0). For all irreducible W-modules those eigenvalues are computed in [3]. For irreducible W-modules L i (i = 1, 2, 3), set…”

“…is greater than or equal to the multiplicity of W 3 (j 3 ,λ 3 ) in I (j 1 ,λ 1 ),(j 2 ,λ 2 ) . This paper is organized as follows.…”

“…In Section 3 we give a construction of intertwining operators for irreducible V G -modules which occur as submodules of irreducible V -modules. In Section 4 we apply the main result to determine some fusion rules for a vertex operator algebra W studied in [3]. In Appendix, we give some singular vectors in W-modules used in Section 4.…”

The Structure of Parafermion Vertex Operator Algebras: General Case

“…Although the parafermion field theory has been studied for more than two decades, the mathematical investigation of the parafermion vertex operator algebras have been limited by a lack of understanding of the structural theory of these algebras. The goals of this paper and [4][5][6] are to alleviate this situation.…”