2010/10/22 by Ben Walter, Walter, Ben
Mathematics · #16T15 #17B01 #17B35 #17B62 #18D50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1010.4732
openalex publication_date 2010/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the associative Lie polynomial. Our work moves from associative algebras to preLie algebras to graph complexes, justifying the use of graph generators for Lie coalgebras by iteratively expanding the set of generators until the set of relations collapses to two simple local expressions. Our focus is on new computational methods allowed by this framework and the efficiency of the graph presentation in proofs and calculus involving free Lie algebras and coalgebras. This outlines a new way of understanding and calculating with Lie algebras arising from the graph presentation of Lie coalgebras.