Vertex Operator Algebras
VOAs, conformal field theory, and the monstrous moonshine.
Vertex Operator Algebras. VOAs, conformal field theory, and the monstrous moonshine.
Foundations and canonical references
The standard treatments of vertex operator algebras approach the subject from complementary angles. Frenkel, Vertex Algebras and Algebraic Curves (2004) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Frenkel, Vertex Operator Algebras and the Monster (1988) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for vertex operator algebras include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2004Vertex Algebras and Algebraic Curvesfrenkel-edward-2004, ben-zvi-2004
- textbook · primary · 1988Vertex Operator Algebras and the Monsterfrenkel-igor-1988, lepowsky-1988, meurman-1988
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