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On axiomatic approaches to vertex operator algebras and modules. (English) Zbl 0789.17022
Mem. Am. Math. Soc. 494, 64 p. (1993).
The problem of realizing the Monster sporadic group as a symmetry group of a certain infinite-dimensional graded vector space led to the discovery of a new class of algebraic object known as “vertex operator algebras”. For a historical discussion about the discovery of this fundamental algebraic object see the Introduction in the book [I. Frenkel, J. Lepowsky and A. Meurman, “Vertex Operator Algebras and the Monster” (Pure Appl. Math. 134) (Academic Press, 1988; Zbl 0674.17001)].
In this paper, the authors further develop the abstract theory of vertex operator algebras and their representations in a rigorous manner. The importance of these new algebras and their representations is supported by their numerous connections with other areas in mathematics and physics.

MSC:
17B69 Vertex operators; vertex operator algebras and related structures
17B68 Virasoro and related algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B65 Infinite-dimensional Lie (super)algebras
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