Equivalence of Borcherds GVertex Algebras and Axiomatic Vertex Algebras
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1999
 arXiv:
 arXiv:math/9904104
 Bibcode:
 1999math......4104S
 Keywords:

 Quantum Algebra;
 Category Theory;
 Mathematical Physics
 EPrint:
 36 pages, amslatex, epsfig, Xypic