A vertex operator algebra is an algebraic structure that encodes the symmetries of two-dimensional conformal field theories, often used in string theory and related areas. It provides a rigorous mathematical framework for the study of vertex operators, which are central to the formulation of these theories and their associated representation theory.

Vertex Operator Algebra

An algebraic structure is a set equipped with one or more operations that follow specific axioms, providing a framework to study algebraic systems like groups, rings, and fields. These structures allow mathematicians to abstract and generalize patterns and properties across different mathematical systems, facilitating deeper understanding and applications across various domains.

Algebraic Structure

Symmetries of two-dimensional conformal field theories

String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects known as strings. It aims to reconcile general relativity and quantum mechanics, potentially providing a unified description of all fundamental forces and particles in the universe.

String Theory

Mathematical Framework

Study of vertex operators

Formulation of theories

Representation Theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. This approach allows complex algebraic problems to be translated into more manageable linear algebra problems, providing deep insights into the symmetry and structure of mathematical objects.

Concepts

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