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hal-00563485, version 1

ALGEBRAS DETERMINED BY THEIR SUPPORTS

Ibrahim Assem () 1, Diane Castonguay () 2, Marcelo Lanzilotta () 3, Rossana Vargas () 4

(01/2011)

Résumé : In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander-Reiten components of an ada algebra, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes.

  • 1 :  Département de mathématiques, Université de Sherbrooke
  • Université de Sherbrooke
  • 2 :  Instituto de Informática da UFRGS (UFRGS)
  • Universidade Federal do Rio Grande do Sul
  • 3 :  Instituto de Matemática y Estadística Rafael Laguardia (IMERL)
  • Universidad de la República Uruguay
  • 4 :  Escola de Artes Ciências e Humanidades (EACH)
  • Universidade de São Paulo
  • Domaine : Mathématiques/Théorie des représentations
  • Mots-clés : Representation theory – Module category – artin algebras
 
  • hal-00563485, version 1
  • http://hal.archives-ouvertes.fr/hal-00563485
  • oai:hal.archives-ouvertes.fr:hal-00563485
  • Contributeur : Marcelo Lanzilotta <>
  • Soumis le : Dimanche 6 Février 2011, 02:50:50
  • Dernière modification le : Dimanche 6 Février 2011, 20:23:38