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A note on the fundamental group of a one-point extension

  • Assem, Ibrahim [1] ; Bustamante, Juan Carlos [1] ; Castonguay, Diane [2] ; Novoa Bustos, Cristian [3]
    1. [1] Université de Sherbrooke

      Université de Sherbrooke

      CA.10.05.43027, Canadá

    2. [2] Universidade Federal de Goiás

      Universidade Federal de Goiás

      Brasil

    3. [3] Pontifícia Universidade Católica de Goiás

      Pontifícia Universidade Católica de Goiás

      Brasil

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 79-87
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172005000100007
  • Enlaces
  • Resumen
    • In this note, we consider an algebra A which is a one-point extension of another algebra B and we study the morphism of fundamental groups induced by the inclusion of (the bound quiver of ) B into (that of ) A. Our main result says that the cokernel of this morphism is a free group and we prove some consequences from this fact.

  • Referencias bibliográficas
    • Citas [1] I. Assem, D. Castonguay, E. N. Marcos, and S. Trepode. Schurian strongly simply connected algebras and multiplicative bases. J....
    • [2] I. Assem and J.A. de la Peña. The fundamental groups of a triangular algebra. Comm. Algebra, 24 (1) : pp. 187—208, (1996).
    • [3] K. Bongartz and P. Gabriel. Covering spaces in representation theory. Invent. Math, 65 (3) : pp. 331—378, (1981)-(1982).
    • [4] M. J. Bardzell and E. N. Marcos. H1(Λ) and presentations of finite dimensional algebras. Number 224 in Lecture Notes in Pure and Applied...
    • [5] J. C. Bustamante. On the fundamental group of a schurian algebra. Comm. Algebra, 30 (11) : pp. 5305—5327, (2002).
    • [6] J. C. Bustamante. The classifying space of a bound quiver. J. Algebra, 277 : pp. 431—455, (2004).
    • [7] R. Martínez-Villa and J.A. de la Peña. The universal cover of a quiver with relations. J. Pure Appl. Algebra, 30 : pp. 873—887, (1983).
    • [8] A. Skowronski. Simply connected algebras and Hochschild cohomologies. In Proceedings of the sixth international conference on representation...

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