Iterated coil enlargements of algebras

Bertha Tomé

Fundamenta Mathematicae (1995)

  • Volume: 146, Issue: 3, page 251-266
  • ISSN: 0016-2736

Abstract

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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form q Λ of Λ is weakly non-negative, (c) Λ is an iterated coil enlargement

How to cite

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Tomé, Bertha. "Iterated coil enlargements of algebras." Fundamenta Mathematicae 146.3 (1995): 251-266. <http://eudml.org/doc/212065>.

@article{Tomé1995,
abstract = {Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form $q_Λ$ of Λ is weakly non-negative, (c) Λ is an iterated coil enlargement},
author = {Tomé, Bertha},
journal = {Fundamenta Mathematicae},
keywords = {finite-dimensional basic connected algebras; categories of finitely generated right modules; indecomposable projective modules; preprojective components; standard coils; Tits forms; iterated coil enlargements},
language = {eng},
number = {3},
pages = {251-266},
title = {Iterated coil enlargements of algebras},
url = {http://eudml.org/doc/212065},
volume = {146},
year = {1995},
}

TY - JOUR
AU - Tomé, Bertha
TI - Iterated coil enlargements of algebras
JO - Fundamenta Mathematicae
PY - 1995
VL - 146
IS - 3
SP - 251
EP - 266
AB - Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form $q_Λ$ of Λ is weakly non-negative, (c) Λ is an iterated coil enlargement
LA - eng
KW - finite-dimensional basic connected algebras; categories of finitely generated right modules; indecomposable projective modules; preprojective components; standard coils; Tits forms; iterated coil enlargements
UR - http://eudml.org/doc/212065
ER -

References

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  9. [9] J. A. de la Pe na, On the representation type of one-point extensions of tame concealed algebras, Manuscripta Math. 61 (1988), 183-194. Zbl0647.16021
  10. [10] J. A. de la Pe na and B. Tomé, Iterated tubular algebras, J. Pure Appl. Algebra 64 (1990), 303-314. Zbl0704.16006
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  12. [12] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part I, PWN, Warszawa, 1990, 535-568. 
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