ON THE CORANK OF THE TITS FORM OF A TAME ALGEBRA

Let Lambda = k[Q]/I be a finite-dimensional, directed k-algebra with k an algebraically closed field. Let q(Lambda) be the Tits (quadratic) form of it. The isotropic corank of q(Lambda), denoted by corank(0) q( Lambda), is the maximal dimension of a convex half-space over Q contai ned in Sigma(0)(q(Lambda)) = {0 less than or equal to nu is an element of Q(n): q(Lambda)(nu) = 0}, where n is the number of vertices of Q. We show that a strongly simply connected cycle-finite algebra Lambda, has corank(0)q(Lambda) less than or equal to 2. A strongly simply conn ected algebra Lambda is tame domestic if and only if q, is weakly non- negative and corank(0) q(Lambda) less than or equal to 1. We also char acterize polynomial growth algebras using invariants associated with t he Tits form.