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On certain higher dimensional analogues of vertex algebras

Haisheng Li
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Abstract

A higher dimensional analogue of the notion of vertex algebra is formulated in terms of formal variable language with Borcherds' notion of $G$-vertex algebra as a motivation. Some examples are given and certain analogous duality properties are proved. Furthermore, it is proved that for any vector space $W$, any set of mutually local multi-variable vertex operators on $W$ in a certain canonical way generates a vertex algebra with $W$ as a natural module.

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Haisheng Li. 2001-04-24. On certain higher dimensional analogues of vertex algebras. https://arxiv.org/abs/math/0104225

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