Abstract
Inspired by Borcherds' work on "G-vertex algebras," we formulate and study an axiomatic counterpart of Borcherds' notion of G-vertex algebra for the simplest nontrivial elementary vertex group, which we denote by G1. Specifically, we formulate a notion of axiomatic G1-vertex algebra, prove certain basic properties and give certain examples, where the notion of axiomatic G1-vertex algebra is a nonlocal generalization of the notion of vertex algebra. We also show how to construct axiomatic G1-vertex algebras from a set of compatible G1-vertex operators.
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