Prinjective Ringel-Hall algebras for posets of finite prinjective type. (Q839744)

Let \(I\) be a finite partially ordered set. Assume that there exist only finitely many isomorphism classes of indecomposable prinjective modules over the incidence algebra of \(I\). The main result of this paper gives a presentation of the generic prinjective Ringel-Hall algebra of \(I\) by generators and relations. The generators are indexed by elements of \(I\). There are five types of relations: commutativity for incomparable elements; \(q\)-commutativity for comparable elements, non of which is maximal; (two) Serre-type relations for comparable elements, one of which is maximal; and a Serre type relation involving three linearly ordered elements, one of which is maximal.