Vertex Coalgebras, Co-Associator and Co-Commutator formulas

TL;DR

This paper reformulates the concept of vertex coalgebras using Co-Commutator, Co-Skew symmetry, and Co-Associator formulas, removing previous grading restrictions, thereby providing a more general framework.

Contribution

It introduces a new formulation of vertex coalgebras that eliminates grading restrictions, enhancing theoretical understanding and potential applications.

Findings

Reformulation of vertex coalgebras without grading restrictions

Establishment of Co-Commutator, Co-Skew symmetry, and Co-Associator formulas

Simplified axiomatic framework for vertex coalgebras

Abstract

Based on the definition of vertex coalgebra introduced by Hubbard [H], we prove that this notion can be reformulated using the Co-Commutator, Co-Skew symmetry and Co-Associator formulas without restrictions on the grading.