Combinatorial Formulas for Classical Lie Weight Systems on Arrow Diagrams
نویسنده
چکیده
In [Ha] 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 ([BN1]). In the last section we carry out calculations on certain examples.
منابع مشابه
Classical Lie Algebra Weight Systems of Arrow Diagrams by Louis Leung A
Classical Lie Algebra Weight Systems of Arrow Diagrams Louis Leung Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2010 The notion of finite type invariants of virtual knots introduced in [GPV] leads to the study of ~ An, the space of diagrams with n directed chords mod 6T (also known as the space of arrow diagrams), and weight systems on it. It is well known that ...
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