On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras

Abstract

We describe an approach to classify (meromorphic) representations of a given vertex operator algebra by calculating Zhu's algebra explicitly. We demonstrate this for FKS lattice theories and subtheories corresponding to the Z_2 reflection twist and the Z_3 twist. Our work is mainly offering a novel uniqueness tool, but, as shown in the Z_3 case, it can also be used to extract enough information to construct new representations. We prove the existence and some properties of a new non-unitary representation of the Z_3-invariant subtheory of the (two dimensional) Heisenberg algebra.

60 pages, Latex

References in corpus (2)

• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice

Cited by in corpus (2)

• Certain associative algebras similar to $U(s{l}_2)$ and Zhu's algebra $A(V_L)$
• Zhu's Theorem and an algebraic characterization of conformal blocks