On the corank of the Tits form of a tame algebra Original Research Article

Let Λ = k[Q]/I be a finite-dimensional, directed k-algebra with k an algebraically closed field. Let qΛ be the Tits (quadratic) form of Λ. The isotropic corank of qΛ denoted by corank0 qgL, is the maximal dimension of a convex half-space over image contained in Σ0(qΛ = {0 ≤ ν ε imagen: qΛ(ν) = 0}, where n is the number of vertices of Q. We show that a strongly simply connected cycle-finite algebra Λ, has corank0qΛ ≤ 2. A strongly simply connected algebra Λ is tame domestic if and only if qgL is weakly non-negative and corank0 qΛ ≤ 1. We also characterize polynomial growth algebras using invariants associated with the Tits form.