# A characterization of representation-finite algebras

Andrzej Skowroński; M. Wenderlich

Fundamenta Mathematicae (1991)

- Volume: 140, Issue: 1, page 31-34
- ISSN: 0016-2736

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topSkowroński, Andrzej, and Wenderlich, M.. "A characterization of representation-finite algebras." Fundamenta Mathematicae 140.1 (1991): 31-34. <http://eudml.org/doc/211926>.

@article{Skowroński1991,

abstract = {Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation.},

author = {Skowroński, Andrzej, Wenderlich, M.},

journal = {Fundamenta Mathematicae},

keywords = {finite-dimensional, basic, connected algebra; Auslander-Reiten quiver; representation-finite; Auslander-Reiten translation},

language = {eng},

number = {1},

pages = {31-34},

title = {A characterization of representation-finite algebras},

url = {http://eudml.org/doc/211926},

volume = {140},

year = {1991},

}

TY - JOUR

AU - Skowroński, Andrzej

AU - Wenderlich, M.

TI - A characterization of representation-finite algebras

JO - Fundamenta Mathematicae

PY - 1991

VL - 140

IS - 1

SP - 31

EP - 34

AB - Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation.

LA - eng

KW - finite-dimensional, basic, connected algebra; Auslander-Reiten quiver; representation-finite; Auslander-Reiten translation

UR - http://eudml.org/doc/211926

ER -

## References

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