The notion of vertex operator coalgebra and a geometric interpretation

Details The notion of vertex operator coalgebra and a geometric interpretation The notion of vertex operator coalgebra and a geometric interpretation

2004-05-24

arxiv.org/abs/math/0405461v2

Mathematics

Quantum Algebra

46 pages, several proofs added/extended, additional remarks

Scientific paper

The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures meromorphically induced by conformal equivalence classes of worldsheets. We then show this category is isomorphic to the category of vertex operator coalgebras, which is defined in the language of formal algebra. The latter has several characteristics which give it the flavor of a coalgebra with respect to the structure of a vertex operator algebra and several characteristics that distinguish it from a standard dual -- both will be mentioned.

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