We explain a direct topological proof for the multiplicativity of the Duflo isomorphism
for arbitrary finite-dimensional Lie algebras, and derive the explicit formula for the
Duflo map. The proof follows a series of implications, starting with “the calculation
on a 4D
abacus”, using the study of
homomorphic expansions (aka universal finite-type invariants) for
ribbon
–knots,
and the relationship between the corresponding associated graded space
of
arrow diagrams and universal enveloping algebras. This complements
the results of the first author, Le and Thurston, where similar arguments
using a “3D abacus” and the Kontsevich integral were used to deduce Duflo’s
theorem for
metrized Lie algebras; and results of the first two authors on
finite-type invariants of w–knotted objects, which also imply a relation of
–knots
with the Duflo theorem in full generality, though via a lengthier path.
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