Vertex Coalgebras, Coassociator, and Cocommutator Formulas

Abstract

Based on the definition of vertex coalgebra introduced by Hubbard, 2009, we prove that this notion can be reformulated usingcoskew symmetry, coassociator and cocommutator formulas without restrictions on the grading. We also prove that a vertexcoalgebra can be defined in terms of dual versions of the axioms of Lie conformal algebra and differential algebra.