Let A = kQ/I be a finite dimensional basic algebra over an algebraically closed field k presented by its quiver Q with relations I. A fundamental problem in the representation theory of algebras is to decide whether or not A is of tame or wild type. In this paper we consider triangular algebras A whose quiver Q has no oriented paths. We say that A is essentially sincere if there is an indecomposable (finite dimensional) A-module whose support contains all extreme vertices of Q. We prove that if A is an essentially sincere strongly simply connected algebra with weakly non-negative Tits form and not accepting a convex subcategory which is either representation-infinite tilted algebra of type Êp or a tubular algebra, then A is of polynomial growth (hence of tame type).
@article{urn:eudml:doc:41872,
title = {Substructures of algebras with weakly non-negative Tits form.},
journal = {Extracta Mathematicae},
volume = {22},
year = {2007},
pages = {67-81},
zbl = {1151.16013},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41872}
}
Peña, José Antonio de la; Skowronski, Andrzej. Substructures of algebras with weakly non-negative Tits form.. Extracta Mathematicae, Tome 22 (2007) pp. 67-81. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41872/