A higher-dimensional generalization of the notion of vertex algebra

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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.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalJournal of Algebra
Issue number1
StatePublished - Apr 1 2003

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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