On the action of the symmetric group on the Free Lie Algebra and on the homology and cohomology of the partition lattice.

摘要

he Free Lie Algebra over an alphabet A, denoted here by LIE (A), is the smallest subspace of the linear span of the A-words which contains the letters and is closed under the bracket operation (f,g) = fg ;It follows from recent work of Stanley and Joyal that this action and the action of ;More precisely we chose the Lyndon basis for LIE (A), and for the Stanley-Reisner ring of