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arXiv · 1711.05343

On Infinite Order Simple Current Extensions of Vertex Operator Algebras

Jean Auger·Matt Rupert
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Abstract

We construct a direct sum completion $\mathcal{C}_{\oplus}$ of a given braided monoidal category $\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of vertex operator algebras as seen in \cite{CKL}. As an example, we construct the vertex operator algebra $V_L$ associated to an even lattice $L$ as an infinite order simple current extension of the Heisenberg VOA and recover the structure of its module category through categorical considerations.

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Jean Auger, Matt Rupert. 2017-11-14. On Infinite Order Simple Current Extensions of Vertex Operator Algebras. https://arxiv.org/abs/1711.05343

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