The Orlik-Solomon algebra on the partition lattice and the free Lie algebra (Q921099)

The authors prove that the actions of the symmetric group \(S_ n\) on the exterior algebra of the free Lie algebra and on the Orlik-Solomon algebra of the partition lattice are equivalent up to tensoring with the sign representation. This is done by constructing an explicit basis in each of those spaces and creating a link between those spaces by developing a natural bijection between the constructed bases of the spaces.