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Nonassociativity in VOA theory and finite group theory. (English) Zbl 1224.17033

The paper summarizes basic properties of vertex oriented algebras and their connections to (sporadic) groups. It points out the role of nonassociativity and suggests several research lines that might pursued by nonassociative theorists.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
20D06 Simple groups: alternating groups and groups of Lie type
20D08 Simple groups: sporadic groups
17A01 General theory of nonassociative rings and algebras
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)