Vertex Algebras

  1. Affine Vertex Algebras
    1. Affine Kac-Moody Algebras
      1. Loop Algebra Construction
        1. Central Extension
          1. Cartan Subalgebra
            1. Root System Structure
              1. Weyl Group Action
              2. Vacuum Representations
                1. Highest Weight Theory
                  1. Verma Modules
                    1. Irreducible Quotients
                      1. Character Formulas
                      2. Vertex Algebra Structure
                        1. State-Field Correspondence
                          1. Current Fields
                            1. OPE Relations
                              1. Mode Algebras
                              2. Sugawara Construction
                                1. Energy-Momentum Tensor
                                  1. Sugawara Operators
                                    1. Virasoro Relations
                                      1. Central Charge Formula
                                        1. Coset Constructions

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                                      6. Fundamental Examples

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                                      8. Virasoro and Conformal Structure