Vertex Algebras

  1. Basic Structure of Vertex Algebras
    1. The State Space
      1. Vector Space Structure
        1. Grading Properties
          1. Filtration Concepts
            1. Basis Considerations
              1. Dimension Theory
              2. State-Field Correspondence
                1. The Vertex Operator Map
                  1. Field Notation Y(a,z)
                    1. Mode Expansions
                      1. Locality Properties
                        1. Field Algebra Structure
                        2. Fundamental Elements
                          1. The Vacuum Vector
                            1. Definition and Uniqueness
                              1. Vacuum Properties
                                1. Role in Constructions
                                2. The Translation Operator
                                  1. Definition and Action
                                    1. Derivation Properties
                                      1. Commutation Relations
                                        1. Infinitesimal Translations

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                                    2. Mathematical Preliminaries

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                                    4. Axioms and Fundamental Properties