Combinatorial Formulas for Classical Lie Weight Systems on Arrow Diagrams

2008/12/12 by Louis Leung, Leung, Louis · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0812.2342

openalex publication_date 2008/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2002 Haviv gave a way of assigning Lie tensors to directed trivalent graphs. Weight systems on oriented chord idagrams modulo 6T can then be constructed from such tensors. In this paper we give explicit combinatorial formulas of weight systems using Manin triples constrcted from classical Lie algebras. We then compose these oriented weight systems with the averaging map to get weight systems on unoriented chord diagrams and show that they are the same as the ones obtained by Bar-Natan in 1991. In the last section we carry out calculations on certain examples.

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