A pairing between graphs and trees

Details A pairing between graphs and trees A pairing between graphs and trees

2005-02-25

arxiv.org/abs/math/0502547v3

Mathematics

Quantum Algebra

Material on the Poisson operad has been clarified

Scientific paper

We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson operads, providing canonical duals. In the course of showing that this pairing is perfect we reprove some standard facts about the modules Lie(n), establishing standard bases as well as giving a new means to reduce to those bases. We then move on to define duals to free Lie algebras and to develop product, coproduct and operad structures. We give a brief account here to be built on in a number of different directions in future work.

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