 Author
 Year
 2015
 Title
 On Lie algebra weight systems for 3graphs
 Journal
 Journal of Pure and Applied Algebra
 Volume  Issue number
 219  10
 Pages (fromto)
 45974606
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

A 3graph is a connected cubic graph such that each vertex is equipped with a cyclic order of the edges incident with it. A weight system is a function f on the collection of 3graphs which is antisymmetric: f (H) = f(G) if H arises from G by reversing the orientation at one of its vertices, and satisfies the IHXequation: [graphic]
Key instances of weight systems are the functions phi(g) obtained from a metric Lie algebra g by taking the structure tensor c of g with respect to some orthonormal basis, decorating each vertex of the 3graph by c, and contracting along the edges. We give equations on values of any complexvalued weight system that characterize it as complex Lie algebra weight system. It also follows that if f = phi g for some complex metric Lie algebra g, then f = phi(g), for some unique complex reductive metric Lie algebra g'. Basic tool throughout is geometric invariant theory.
 URL
 go to publisher's site
 Language
 English
 Permalink
 http://hdl.handle.net/11245/1.494183
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