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The notion of vertex operator coalgebra and a geometric interpretation. (English) Zbl 1106.17037

The author defines and investigates the notion of a vertex operator coalgebra as motivated through the geometry of conformal field theory. It is shown that the category of vertex operator coalgebras is isomorphic to the category of geometrically defined structures, which the author calls geometric vertex operator coalgebras. This isomorphism is constructive. The author presents several arguments showing why finding a coalgebra structure in this context is more subtle than just “dualizing” the construction of vertex operator algebras.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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