Vectorspace categories immersed in directed components

Abstract

It is known that, given a tame algebra Λ, the Tits form qΛ is weakly non negative

Moreover, the converse has been shown for some families of algebras, but it is not true in general. The purpose of this work is to show that for certain wild vectorspace categories K = Hom(M,B - mod) where B is tame and M is an indecomposable B-module, we have qB[M] strongly indefinite. This gives partial converses of the above theorem.