Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras

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dc.creatorSnydal, Craig T.
dc.date1999-04-20
dc.date.accessioned2026-07-07T05:28:45Z
dc.date.available2026-07-07T05:28:45Z
dc.descriptionIn this paper we build an abstract description of vertex algebras from their basic axioms. Starting with Borcherds' notion of a vertex group, we naturally construct a family of multilinear singular maps parameterised by trees. These singular maps are defined in a way which focusses on the relations of singularities to their inputs. In particular we show that this description of a vertex algebra allows us to present generalised notions of rationality, commutativity and associativity as natural consequences of the definition. Finally, we show that for a certain choice of vertex group, axiomatic vertex algebras correspond bijectively to algebras in the relaxed multilinear category of representations of a vertex group.
dc.description36 pages, amslatex, epsfig, Xy-pic
dc.identifierhttps://arxiv.org/abs/math/9904104
dc.identifierhttp://arxiv.org/abs/math/9904104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78379
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectCategory Theory
dc.titleEquivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras
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