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

Klaus Lucke

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arXiv · hep-th/9605020

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

Klaus Lucke

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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.

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Klaus Lucke. 1996-05-03. On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras. https://arxiv.org/abs/hep-th/9605020

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