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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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IV.17 Vertex Operator Algebras

Terry Gannon

1 Introduction

Algebra is the mathematics that places more emphasis on abstract structure than on intrinsic meaning. The conceptual simplifications that can result when context is stripped away from structure give algebra a special power and clarity compared with other areas: compare, for example, the difficulty of visualizing four-dimensional space with the triviality of manipulating quadruples (x1, x2, x3, x4) of real numbers. However, this abstractness can also blind us. For instance, basic identities like ab = ba and a(bc) = (ab)c that are obeyed by numbers can be modified in countless directions, and each modification defines a new algebraic structure, but it is hard to guess from a purely abstract ...

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