Vertex coalgebras, comodules, cocommutativity and coassociativity

Details Vertex coalgebras, comodules, cocommutativity and coassociativity Vertex coalgebras, comodules, cocommutativity and coassociativity

2008-01-21

arxiv.org/abs/0801.3260v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, $D^*$, which hold on vertex coalgebras. The former two properties require grading. We then discuss comodule structure. We conclude by discussing instances where graded vertex coalgebras appear, particularly as related to Primc's vertex Lie algebra and (universal) enveloping vertex algebras.

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