Three-partite subamalgams of tiled orders of finite lattice type Original Research Article

Let D be a complete discrete valuation domain with the residue field K. We study in the paper a class of subamalgams Λ• (1.3) of tiled D-orders Λ (1.1) by means of an integral quadratic Tits form image and a matrix problem over K defined in Section 3 by a finite stratified poset Ip associated with Λ•. Simple criteria for the finite lattice type of Λ• are given in terms of the Tits form qΛ•, in terms of a two-peak poset (IΛ•*+, 3Λ•) with zero-relations associated to Λ• in (4.4), and in terms of forbidden minor D-suborders of Λ• presented in Table 1. The shape of Auslander-Reiten quiver Γ(latt(Λ•)) is described in Remarks 6.4.