Alternative Definitions
Another way to think of vertex algebras is as a generalisation of a Lie algebra with the addition of a continuous variable to both the generators of the algebra and the structure constant. (The structure constants define the algebra). So we would have:
which can also be expressed without the y dependence as:
which reveals the Vertex Multiplication as a group operation in which the group constants vary with their position on the conformal sheet.
Read more about this topic: Vertex Operator Algebra
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