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Combining the two propositions
weight systems are associated graded of Vassiliev invariants,
weight systems are cohomology of loop space of configuration space
we get this situation.
Hope I got this right…
added a pointer to Lie algebra weight systems:
A large class of weight systems arises from reading a (horizontal) chord diagram as a string diagram in the evident way, and then labelling it by the structure morphisms of a Lie algebra object equipped with a Lie algebra representation internal to a suitable tensor category. This does yield weight systems because the required relations translate exactly to the structural equations satisfied by Lie modules (Jacobi identity and Lie action property).
The weight systems arising this way are called Lie algebra weight systems. See there for more
added pointer to
re-organized subsections: split off “Constructions of weight systems” from “Properties”; added stub section on stringy weight systems
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