Vertex Algebras

9.

Module Theory and Representations

9.1.

Vertex Algebra Modules

9.1.1.

9.1.2.

9.1.3.

Admissible Modules

9.1.4.

Examples and Constructions

9.2.

Module Categories

9.2.1.

Morphisms of Modules

9.2.2.

Submodules and Quotients

9.2.3.

9.2.4.

Semisimple Modules

9.2.5.

Indecomposable Modules

9.3.

Contragredient Modules

9.3.1.

Dual Space Construction

9.3.2.

Contragredient Action

9.3.3.

Self-Dual Modules

9.3.4.

Duality Functors

9.4.

Tensor Products

9.4.1.

Tensor Product Construction

9.4.2.

Universal Property

9.4.3.

9.4.4.

Braiding Structure

9.5.

Specific Module Examples

9.5.1.

9.5.2.

9.5.3.

Integrable Modules

9.5.4.

Twisted Modules

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10. Advanced Constructions