2005/02/25 by Dev Sinha, Sinha, Dev P. · 5 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.math/0502547
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.