Formal sums over a vector space

Degree operator on formal sums over a vector space

Let be a vector space over and denote formal sums over . We define the -degree operator¹ fcalc

where is the Formal derivative. This is not strictly a degree operator, as is not a graded vector space, however its subspaces and are.

Properties

Over a graded vector space

Now taking to be -graded with degree operator , and letting

we have

With the formal Dirac delta

Let denote the Formal delta. Then it follows from Properties that for any and

and that for any such that exists and

where and .

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Footnotes

1. 1988. Vertex operator algebras and the Monster, pp. 56–58 ↩