Three-partite subamalgams of tiled orders of finite lattice type

Abstract

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 q Λ • : Z m → Z (1.4) and a matrix problem over K defined in Section 3 by a finite stratified poset I p associated with Λ •. Simple criteria for the finite lattice type of Λ • are given in terms of the Tits form q Λ • , in terms of a two-peak poset ( I Λ • ∗+, 3 Λ • ) 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.