Abstract :
Given a poset P on the set {1,2,…,n}, we define the nilpotent Lie algebra LP to be the span of all elementary matrices zi,j, such that i is less than j in P. We show that for a particular class of partially ordered sets the homology of poset is included in the homology of the corresponding Lie algebra. A necessary condition is that the poset P has both the minimum image and the maximum image.
