Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras

Details Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras

1999-04-20

arxiv.org/abs/math/9904104v1

Mathematics

Quantum Algebra

36 pages, amslatex, epsfig, Xy-pic

Scientific paper

In 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.

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