  Colour-kinematics duality suggests that Yang-Mills (YM) theory possesses some
hidden Lie algebraic structure. So far this structure has resisted
understanding, apart from some progress in the self-dual sector. We show that
there is indeed a Lie algebra behind the YM Feynman rules. The Lie algebra we
uncover is the Drinfeld double of the Lie algebra of vector fields. More
specifically, we show that the kinematic numerators following from the YM
Feynman rules satisfy a version of the Jacobi identity, in that the Jacobiator
of the bracket defined by the YM cubic vertex is cancelled by the contribution
of the YM quartic vertex. We then show that this Jacobi-like identity is in
fact the Jacobi identity of the Drinfeld double. All our considerations are
off-shell. Our construction explains why numerators computed using the Feynman
rules satisfy the colour-kinematics at four but not at higher numbers of
points. It also suggests a way of modifying the Feynman rules so that the
duality can continue to hold for an arbitrary number of gluons. Our
construction stops short of producing explicit higher point numerators because
of an absence of a certain property at four points. We comment on possible ways
of correcting this, but leave the next word in the story to future work.
