Meromorphic open-string vertex algebras

Abstract

A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions for vertex operators. The vertex operator map for a meromorphic open-string vertex algebra satisfies rationality and associativity but in general does not satisfy the Jacobi identity, commutativity, the commutator formula, the skew-symmetry or even the associator formula. Given a vector space \mathfrak{h}, we construct a meromorphic open-string vertex algebra structure on the tensor algebra of the negative part of the affinization of \mathfrak{h} such that the vertex algebra struture on the symmetric algebra of the negative part of the Heisenberg algebra associated to \mathfrak{h} is a quotient of this meromorphic open-string vertex algebra. We also introduce the notion of left module for a meromorphic open-string vertex algebra and construct left modules for the meromorphic open-string vertex algebra above.

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References in corpus (2)

• Open-string vertex algebras, tensor categories and operads
• Meromorphic open-string vertex algebras and Riemannian manifolds

Cited by in corpus (4)

• Meromorphic open-string vertex algebras and Riemannian manifolds
• On modules for meromorphic open-string vertex algebras
• Meromorphic open-string vertex algebras and modules over two-dimensional orientable space forms
• The first cohomology, derivations and the reductivity of a (meromorphic open-string) vertex algebra