A higher-dimensional generalization of the notion of vertex algebra

Haisheng Li

doi:10.1016/S0021-8693(03)00018-8

A higher-dimensional generalization of the notion of vertex algebra

Haisheng Li

FASC - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A higher-dimensional analogue of the notion of vertex algebra, called that of axiomatic G_n-vertex algebra, is formulated with Borcherds' notion of G-vertex algebra as a motivation. Some examples are given and certain analogous duality properties are proved. 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 an axiomatic G_n-vertex algebra with W as a natural module.

Original language	English (US)
Pages (from-to)	1-41
Number of pages	41
Journal	Journal of Algebra
Volume	262
Issue number	1
DOIs	https://doi.org/10.1016/S0021-8693(03)00018-8
State	Published - Apr 1 2003

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/S0021-8693(03)00018-8

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abstract = "A higher-dimensional analogue of the notion of vertex algebra, called that of axiomatic Gn-vertex algebra, is formulated with Borcherds' notion of G-vertex algebra as a motivation. Some examples are given and certain analogous duality properties are proved. 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 an axiomatic Gn-vertex algebra with W as a natural module.",

author = "Haisheng Li",

note = "Funding Information: E-mail address: hli@crab.rutgers.edu. 1 Partially supported by NSF grant DMS-9970496 and a Rutgers Research Council grant.",

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A higher-dimensional generalization of the notion of vertex algebra

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