Dualizing complex of the face ring of a simplicial poset

A finite poset P is called simplicial if it has the smallest element , and every interval is a Boolean algebra. The face poset of a simplicial complex is a typical example. Generalizing the Stanley–Reisner ring of a simplicial complex, Stanley assigned the graded ring AP to P. This ring has been studied from both combinatorial and topological perspectives. In this paper, we will give a concise description of a dualizing complex of AP, which has many applications.