A REDUCTION FUNCTOR, TAMENESS, AND TITS FORM FOR A CLASS OF ORDERS

Let D be a complete discrete valuation domain which is an algebra over an algebraically closed field K. We study in the paper a class of sub orders LAMBDA of tiled D-orders by means of a rational quadratic form q(LAMBDA) associated to LAMBDA and a finite poset I(LAMBDA)+ having e xactly two maximal elements and +. Criteria for finite lattice type and for tame lattice type of LAMBDA are given in terms of the form q(L AMBDA) and of the category I(LAMBDA)+-spr of socle projective K-linea r representations of the poset I(LAMBDA)+. The shape of Auslander-Rei ten quiver GAMMA(latt(LAMBDA)) is described in Corollary 3.2. A reduct ion functor H: latt(LAMBDA) --> I(LAMBDA)+-spr preserving representat ion types is constructed. It is shown in Corollary 2.10 that for any p oset I having exactly two maximal elements there exists a D-order in o ur class, an additive functor latt(LAMBDA) --> I-spr preserving repres entation types and a poset isomorphism I congruent-to I(LAMBDA)+. (C) 1995 Academic Press, Inc.