When is a Lie algebra not a Lie algebra?

Abstract

We look at weight systems on Feynman diagrams. A metric Lie algebra gives one example of a weight system. More generally, a `Casimir Lie algebra object' in an arbitrary linear tensor category also gives a weight system. We look at an example in the category of graded vector spaces coming from the cohomology of a holomorphic symplectic manifold. We then look at how various results for Lie algebras may be rephrased as results for these `Lie algebra objects'.

Appears in the Informal Proceedings of the IXth Oporto Meeting on Geometry, Topology and Physics (available electronically).

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