A Lie Bracket for the Momentum Kernel

Abstract We prove results for the study of double copy and tree-level colour/kinematics duality scattering amplitudes using properties Lie polynomials. show that ‘ S -map’ was defined to simplify super-Yang–Mills multiparticle superfields is in fact a bracket. A generalized KLT map from polynomials their dual obtained by studying our new bracket; matrix elements this yield recently proposed ‘generalized matrix’, reduces usual when its entries are restricted basis. Using this, we give an algebraic proof cancellation poles formula gravity amplitudes. further Berends–Giele recursion biadjoint scalar tree take values Field theory these ‘Lie polynomial amplitudes’ numerators characterized as homomorphisms free algebra kinematic data. Examples presented scalar, Yang–Mills nonlinear sigma model. That theories satisfy Bern–Carrasco–Johansson amplitude relations follows structural prove.