On Tits form and prinjective representations of posets of finite prinjective type

The main aim of this paper is to give an extension of the characterisation given in [18] of finite posets J having only finitely many isomorphism classes of indecomposable socle projective K-linear representations over a given field K. The characterisation is given in Theorem 1.2 and in Theorem 4.1 in terms of the Tits quadratic form associated to J, in terms of the endomorphism rings and self-extensions of indecomposable representations, and in terms of the infinite radical of the category prin(KJ). A converse to a theorem of Bongartz [4] is given in Corollary 3.5.