The Sklyanin bracket and cluster adjacency at all multiplicity

A bstract We argue that the Sklyanin Poisson bracket on Gr(4, n ) can be used to efficiently test whether an amplitude in planar N = 4 supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.