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 characterisa tion given in [18] of finite posets J having only finitely many isomor phism classes of indecomposable socle projective K-linear representati ons 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 indecompo sable representations, and in terms of the infinite radical of the cat egory prin(KJ). A converse to a theorem of Bongartz [4] is given in Co rollary 3.5.