ITERATED COIL ENLARGEMENTS OF ALGEBRAS

Abstract

Let Lambda be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Lambda be the category of finitely generated right Lambda-modules. We say that Lambda has acceptable projectives if the indecomposable projective Lambda-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Lambda the following conditions are equivalent: (a) Lambda is tame, (b) the Tits form q(Lambda) of Lambda is weakly non-negative, (c) Lambda is an iterated coil enlargement.