# Substructures of algebras with weakly non-negative Tits form.

José Antonio de la Peña; Andrzej Skowronski

Extracta Mathematicae (2007)

- Volume: 22, Issue: 1, page 67-81
- ISSN: 0213-8743

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topPeña, 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 -