On the representation type of one point extensions of tame concealed algebras (Q1104395)

Let A be a finite dimensional k-algebra over an algebraically closed field k and \(q_ A\) the Tits quadratic form of A. It is shown that \(q_ A\) is weakly semipositive \((q_ A(z)\geq 0\) for integral vectors z with nonnegative coordinates) whenever A is tame. The main part of the paper is devoted to the proof that, if A is a one-point extension C[R] of a tame concealed algebra C of type \(\tilde D_ n\) or \(\tilde E_ p\) by an indecomposable C-module R, then A is tame iff \(q_ A\) is weakly semipositive. An interesting class of hyperbolic algebras is also considered.