Substructures of algebras with weakly non-negative Tits form.

Peña, José Antonio de la, and Skowronski, Andrzej. "Substructures of algebras with weakly non-negative Tits form.." Extracta Mathematicae 22.1 (2007): 67-81. <http://eudml.org/doc/41872>.

@article{Peña2007,
abstract = {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).},
author = {Peña, José Antonio de la, Skowronski, Andrzej},
journal = {Extracta Mathematicae},
keywords = {tame representation type; essentially sincere modules; Tits forms; strongly simply connected algebras; finite dimensional basic algebras; quivers with relations; triangular algebras; tubular algebras; algebras of polynomial growth},
language = {eng},
number = {1},
pages = {67-81},
title = {Substructures of algebras with weakly non-negative Tits form.},
url = {http://eudml.org/doc/41872},
volume = {22},
year = {2007},
}

TY - JOUR
AU - Peña, José Antonio de la
AU - Skowronski, Andrzej
TI - Substructures of algebras with weakly non-negative Tits form.
JO - Extracta Mathematicae
PY - 2007
VL - 22
IS - 1
SP - 67
EP - 81
AB - 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).
LA - eng
KW - tame representation type; essentially sincere modules; Tits forms; strongly simply connected algebras; finite dimensional basic algebras; quivers with relations; triangular algebras; tubular algebras; algebras of polynomial growth
UR - http://eudml.org/doc/41872
ER -