Simply connected right multipeak algebras and the separation property

Stanisław Kasjan

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 1, page 137-153
  • ISSN: 0010-1354

Abstract

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Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and ˜ -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic form of R.

How to cite

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Kasjan, Stanisław. "Simply connected right multipeak algebras and the separation property." Colloquium Mathematicae 82.1 (1999): 137-153. <http://eudml.org/doc/210746>.

@article{Kasjan1999,
abstract = {Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and $\widetilde\{\}$-free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic form of R.},
author = {Kasjan, Stanisław},
journal = {Colloquium Mathematicae},
keywords = {multipeak path algebras; prinjective modules; almost split sequences; Auslander-Reiten quivers; finite representation type; fundamental groups of bound quivers; Hochschild cohomology},
language = {eng},
number = {1},
pages = {137-153},
title = {Simply connected right multipeak algebras and the separation property},
url = {http://eudml.org/doc/210746},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Kasjan, Stanisław
TI - Simply connected right multipeak algebras and the separation property
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 1
SP - 137
EP - 153
AB - Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and $\widetilde{}$-free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic form of R.
LA - eng
KW - multipeak path algebras; prinjective modules; almost split sequences; Auslander-Reiten quivers; finite representation type; fundamental groups of bound quivers; Hochschild cohomology
UR - http://eudml.org/doc/210746
ER -

References

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